(More than you ever wanted to know about insulating windows without using curtains!)
The plastic makes a HUGE difference. You can get it at any hardware store, and it's a lot cheaper than thermal curtains (well, long run, it's not, because you need to buy new every year, but). They make multi-window packs, and Ace, at least, makes its own brand that costs less than the 3M kind. It's amazing that a piece of plastic that flimsy can provide that much insulation, but it really does. I can always tell, walking into my place, if the cats have sliced through some plastic somewhere, because the temperature difference is that noticeable.
(The cats always go through it. All the cats. Everywhere. You just need to keep tape on hand; it's not pretty, but it's effective. And until they go through, the plastic is basically entirely invisible.)
I have ancient windows that still have the rope sash cords connected to metal weights, which basically sit in these tall uninsulated holes running the length of the window, and which then open up into the window frame at the top. So a few years ago I took to also buying 2-inch-thich foam weather sealer, slicing it in half lengthwise, and sticking each half into the window channel to block as much cold and draft as possible. (Plus also some 1 1/4-inch ones, which I stuff as-is into the usually poor seals between top and bottom windows - nothing in my house is true at this point, so nothing closes properly.) This step is a pain the first time you buy the foam, because it's too thick to cut with scissors; you have to slice it down with a utility knife from both sides, then rip/slice it apart where those two cuts fail to meet in the middle. But once it's the right size, you can reuse the same pieces for several years until the foam starts to go bad.
The plastic itself really isn't hard; the proper way to do it is to clean all the window frames first and go over them with rubbing alcohol for a perfectly clean, good seal, but I gave up on that years ago. The paint on my windows is peeling and crappy, so washing just means I lose lots of paint. So I do overkill instead.
I put the tape from the package up, then put up plastic and cut off the extra around the edges, then before I blow-dry it taut, I go around the entire edge with 2-in wide weatherstrip tape. This helps take care of any spots where the double-sided tape isn't adhering tightly enough, and also cuts down on the amount of damage strong winds can do -- the double-sided tape can actually pull up off the windows just from air pressure. (The plastic sheets bell into the room in wind -- you can totally see them protecting you from bad drafts.) I also wind up putting the plastic up around some odd corners and whatnot, so an extra level of tape can only help.
That tape (and the narrower version you can also buy) is what I use to patch up the holes the cats rip in it, too.
All the plastic comes in unbroken sheets that you cut down to size as you go, so it doesn't matter if your windows aren't standard sizes. If your bay window is also very tall, you can get a package meant for the inside of patio doors.
Most people figure that you can't use your blinds once you put plastic up, unless you figure out a way to put the plastic underneath. This is mostly true! But it also drove me crazy, and one year I had a package that explained how to get around it: you temporarily put the plastic up along the top line of tape, then mark where the blind cord and/or the -- er, turny rod thing -- go, mark circles there with sharpie, then put tape up over the sharpie on both sides of the plastic. (From experience: make ovals, not circles, and make the blind-cord one be horizontal to allow for pulling sideways to release/lock the cord, and make the turny thing vertical to allow for space to lie more flat rather than sticking straight out; make both of them at least an inch longer than you think you'll need.) Remove the turny thing entirely while you have the plastic pulled away to put the tape on it, and pull the blind cord through its hole if you're using it. Then put the plastic up as usual, blow it dry, and put the turny thing back up.
After lots of years of this, I don't bother with the blind cord, and I only leave the turny thing out in half my windows. So half have a perfect seal with no holes, and half have a 2-3-inch hole near the top. It does lead to some airflow, but it's manageable, and lets me have some light if I want it. (If you decide it's too much cold, you can just tape the hole over later.)
It's entirely possible to do an entire house's worth of plastic in one day; I just hate giving up an entire day to house stuff. So I do one room at a time, or even one window at a time, as things get colder. Most years I'm still putting plastic up into late December; it was only that truly vicious cold snap that got me moving so "early" this year. But man, it makes a big difference.
Re: argh, cold.
The plastic makes a HUGE difference. You can get it at any hardware store, and it's a lot cheaper than thermal curtains (well, long run, it's not, because you need to buy new every year, but). They make multi-window packs, and Ace, at least, makes its own brand that costs less than the 3M kind. It's amazing that a piece of plastic that flimsy can provide that much insulation, but it really does. I can always tell, walking into my place, if the cats have sliced through some plastic somewhere, because the temperature difference is that noticeable.
(The cats always go through it. All the cats. Everywhere. You just need to keep tape on hand; it's not pretty, but it's effective. And until they go through, the plastic is basically entirely invisible.)
I have ancient windows that still have the rope sash cords connected to metal weights, which basically sit in these tall uninsulated holes running the length of the window, and which then open up into the window frame at the top. So a few years ago I took to also buying 2-inch-thich foam weather sealer, slicing it in half lengthwise, and sticking each half into the window channel to block as much cold and draft as possible. (Plus also some 1 1/4-inch ones, which I stuff as-is into the usually poor seals between top and bottom windows - nothing in my house is true at this point, so nothing closes properly.) This step is a pain the first time you buy the foam, because it's too thick to cut with scissors; you have to slice it down with a utility knife from both sides, then rip/slice it apart where those two cuts fail to meet in the middle. But once it's the right size, you can reuse the same pieces for several years until the foam starts to go bad.
The plastic itself really isn't hard; the proper way to do it is to clean all the window frames first and go over them with rubbing alcohol for a perfectly clean, good seal, but I gave up on that years ago. The paint on my windows is peeling and crappy, so washing just means I lose lots of paint. So I do overkill instead.
I put the tape from the package up, then put up plastic and cut off the extra around the edges, then before I blow-dry it taut, I go around the entire edge with 2-in wide weatherstrip tape. This helps take care of any spots where the double-sided tape isn't adhering tightly enough, and also cuts down on the amount of damage strong winds can do -- the double-sided tape can actually pull up off the windows just from air pressure. (The plastic sheets bell into the room in wind -- you can totally see them protecting you from bad drafts.) I also wind up putting the plastic up around some odd corners and whatnot, so an extra level of tape can only help.
That tape (and the narrower version you can also buy) is what I use to patch up the holes the cats rip in it, too.
All the plastic comes in unbroken sheets that you cut down to size as you go, so it doesn't matter if your windows aren't standard sizes. If your bay window is also very tall, you can get a package meant for the inside of patio doors.
Most people figure that you can't use your blinds once you put plastic up, unless you figure out a way to put the plastic underneath. This is mostly true! But it also drove me crazy, and one year I had a package that explained how to get around it: you temporarily put the plastic up along the top line of tape, then mark where the blind cord and/or the -- er, turny rod thing -- go, mark circles there with sharpie, then put tape up over the sharpie on both sides of the plastic. (From experience: make ovals, not circles, and make the blind-cord one be horizontal to allow for pulling sideways to release/lock the cord, and make the turny thing vertical to allow for space to lie more flat rather than sticking straight out; make both of them at least an inch longer than you think you'll need.) Remove the turny thing entirely while you have the plastic pulled away to put the tape on it, and pull the blind cord through its hole if you're using it. Then put the plastic up as usual, blow it dry, and put the turny thing back up.
After lots of years of this, I don't bother with the blind cord, and I only leave the turny thing out in half my windows. So half have a perfect seal with no holes, and half have a 2-3-inch hole near the top. It does lead to some airflow, but it's manageable, and lets me have some light if I want it. (If you decide it's too much cold, you can just tape the hole over later.)
It's entirely possible to do an entire house's worth of plastic in one day; I just hate giving up an entire day to house stuff. So I do one room at a time, or even one window at a time, as things get colder. Most years I'm still putting plastic up into late December; it was only that truly vicious cold snap that got me moving so "early" this year. But man, it makes a big difference.