Is eating in the bedroom or any typical part of the bedroom forbidden? I've heard that there's some sort of tumah associated with this action, but couldn't get verification outside of differing opinions on leaving your food under the bed.
I can't find in Shulchan Aruch a prohibition to eat in the bedroom. There is an issue of leaving food under the bed. But as far as eating in the bedroom it seems perfectly permitted.
However, there is a principle in preparing for Pesach (Mishna Pesachim 1:1), that if a bedroom or cellar has not being frequented the whole year - i.e. one is very careful to not eat at all in such a place, the whole year, one need not do a deep cleaning and checking for Chometz, since one was particular in making sure that this area was free from Chometz the whole year. This is perhaps why many families especially prohibit eating in places other than the kitchen and dining space.
Aside from that, it seems a particular culture - derech eretz if you will, of being a mentsch - kings and queens eat in the dining room. You wouldn't expect Queen Elizabeth II to have her lunch in bed, but rather in a dining room or tea room etc. So as far as behaving like a prince of G-d, it is meaningful to eat in the dining room as kavod and respect to Hashem (we're His children) and the house as a whole. But this is purely cultural. People view their bedrooms as their own living spaces (especially children) and certainly have desks and chairs where they study, and eat in those spaces. Does President Trump have a bite to eat in his bedroom? Many people drink coffee in their bedrooms.