Someone help me with a roommate issue?

My roommate is naturally loud and opinionated. I have my opinions, too, but I am generally quieter. In the beginning of this year, I really wanted the bed by the window, but she hadn't arrived yet so I waited for her to get there so we could discuss who would get it. But she got there and plopped her stuff down on the bed. There was no room for negotiation. Since then we've been fine, but it always pissed me off a little. Anyways, this year we're getting an apartment and there are 2 bedrooms. One is significantly bigger than the other, and she wants the big one. I told her that if we're not rooming together (we're not sure yet) then we should draw straws for who gets the big room. She literally shut me down and immediately told me no. She said she had found the place and done all this work to get it, therefore there IS no negotiation– the big room is hers regardless. Am I crazy to say that we're all paying the same amount, so we should draw straws??? I've done a lot of work for this apt. too. How should I tell her it's not okay? (Ya, I know I don't have tough skin.)