A bulge means that the metal has been stretched beyond it's elastic limit. In normal use, the steel expands, but then returns to it's original shape. Excess pressure pushes it past that point where it doesn't return and it stays in the expanded position.
While swaging and a couple of other techniques can be used to bring the outer shape back down again, the cold working of the now over stressed steel does nothing good for the strength in that area. It may produce cracking within the area in a worst case.
Sometimes the bulge will reappear in a bbl repaired in this manner as the steel has lost it's strength from being overstressed first then cold worked again to push it back into place. I've seen it a few times on shotgun bbls.
That's a lot of steel to compress back into position cleanly in full diameter at that point on a rifle bbl.
It can be done with some degree of success on shotgun bbls as they are generally thinner. But even then, if the bulge is back near the breech and chamber areas, it's usually a no-go. Safety of the finished job is the primary reason and shotgun pressures (12ga) are 12K and below.
In the very least the bore will not go back into position, lining up with perfect grooves and lands through that area no matter how good the swage work. It may shoot worse after the 'fix' than it does before.
Shotgun bores have the advantage of being able to be polished out abit to clean them up after the work to improve looks and no rifling to worry about.
If the appearance of the bulge itself bothers you more than it's presence in the bore (rifle shoots OK),,I've seen more than a few where the outside has been cleaned up (bump draw filed off), polished and finish matched up.
How close the bulge is to the chamber end, how much mat'l has been displace (how much will be removed in cleaning it up) will determine if it's safe to do.
If not,,I'd have it relined to 44-40 and at the same time take care of the bulge appearance on the outside and refinish the area to match.
That way you have the original bbl, a pristine bore, and the period finish still on the rifle.