It might not be the biking, but in trying to figure out what is causing this I can't come to any other conclusion. I used to bike 3-6 times a week, with no problems. Now I'm biking about 12 times a week (counting trips to and from work separately). I also noticed I was biking faster than normal, and thought that that might be the culprit.
I've tried biking slower, to no avail.
My diet hasn't changed (that I can think of).
Sometimes I'm biking near heavy traffic, but the burping wasn't a problem in the past on the same route but less often. Hmm.
I tried eating lots of yogurt in case I needed more good bacteria in my stomach. Didn't help.
If there are more ideas, keep em coming! :) I think I've lost weight from biking, but it's hard to notice with the buildup of air in my stomach... Haha oh man.