How to create a bulge shape?

Perhaps you would be interested in the package DynaShape.

I have not personally had much experience using this package, but i have used Kangaroo physics for grasshopper extensively - DynaShape is the Dynamo response to Kangaroo and looks like it would help you generate the sort of relaxed form (doubly-curved, funicular geometry) you refer to as a ‘Bulge’.