Very interesting discussion. I concur in that I would not want to mess with a bulge close to the chamber.
As to a bulge closer to the muzzle, after inspection with a knowledgeable person I would not be afraid. I had such a shotgun with twist barrels that had a bulge and a split about 5 inches from the muzzle on the bottom of the left barrel. With the concurrence of an individual with far more experience than I the the bulge was beaten down on a mandrel. I then took the barrelset to a local welder who told me to machine a piece of copper to fit snugly under the weld. He welded it and after dressing the weld I use the gun as my clays gun without a problem.
My point 1. The bulge was close to the muzzle and 2. I had a knowledgeable person look at it.