Off-center
As soon as I read that the bulge was only on one side, I thought of something similar to jibjab, but read through the thread to make sure no one else suggested it already.
First question: Is the bulge always the same orientation when you cartridge comes out of the press? This points to the die (as jibjab suggests) as the source, or the press itself (either the shell holder, the ram or the press' frame).
Try this. Ensure the shell holder is all the way installed on the ram and centered. Then make sure the cartridge case is all the way into the shell holder. After you insert it, give it an extra, gentle push with just your fingertip, very near the base. See if that cures the asymmetric bulge.
If that doesn't cure it, try turning the shell holder 90 degrees and seat a few more. If the orientation/direction of the bulge changes, the shell holder is suspect.
Another experiment is to back the die body out a couple of turns and the seating stem in by the same amount. Seat a few rounds (without crimp, obviously, since you backed the body out). Is the bulge still there and one-sided just as before?
After you get the bullets seated, you can back the seating stem (all the way) out and apply the (taper) crimp alone.
If you REALLY suspect the brass thickness being the reason the bulge is asymmetrical, try this: Mark a couple of cases to show where the bulge is. (Mark on the case head; a mark on the side of the case may come off during sizing.) Size those cases, do not prime or powder them, but bell the case mouth. By hand, insert and seat a bullet (you will probably have to use a light hammer to tap it in unless you have a vice or c-clamp). The idea is to separate die alignment from the experiment. If you find a bulge in the same position as it was before, I would strongly suspect the brass thinness is the reason for the asymmetric bulge.
Ain't science fun?
Lost Sheep