What size breaker should I use to feed an electrical panel for our addition?
Each baseboard heater is probably 15A (if not then check what they actually are), and the dryer is 30A. So you're already at 90A. The washer (is it frontloading?) will need 15A/2 (it's 120V), and so will the bathroom, so that's 105A. I can easily imagine all those running at once. Then you have some plugs and whatnot, but you probably won't max all of them at once.

Looks like 120A will be OK, but just barely. Is electrical heat really your only option? Can you use a gas dryer?