No, I wouldn't say that Nick Bottom is upset with Quince. I went back and reread that part, and I can see why the question is being asked. Bottom is continually asking to play each part of the play because he thinks that he would be able to play it better than the other men. It's silly because he seems to think that he is capable of performing the entire play all by his lonesome. If I had to pick an attitude of Nick Bottom's, it would be cocky. He just seems to think that he is the best at everything.
If anybody has the right to be upset, it's Quince. He has obviously spent time figuring out which person should play which part based on what he believes is each man's strength. So when Bottom is continually interrupting Quince, it makes sense that Quince would get annoyed.