Harriger55, First off welcome to the board! Second is, How big is the bulge and have you had a good double-gunsmith look at it?
Bulges depending on size and placement quite often can be repaired by someone who knows what they are doing. The big kicker is if the bulge separated the barrel at the rib joint.
Replacement barrels will be expensive & that's if you can find a set. First you have to purchase them, then you have to have them fit to the gun "if they will fit at all" more than likely they will need to be blued, Etc. There are some new old stock in the white barrels floating around. Most of these need one heck of a lot of work done to them and for a Sterlingworth it would be cost prohibitive. There is the option of sleeving, but that will start at about $2000.00
My suggestion is to call one of our members here Steve Bertram "SKB" 303-938-1996 and talk over your options with him. Steve is a great guy and a good double-gunsmith that won't steer you wrong.