As noted above, don't worry about bulged cases and potential case web failures with the .38 Special.
A bulged case is common in a revolver that has been converted from .38 SW (.38-200 in British service) to the longer but slightly smaller base diameter .38 S&W Special (called plain old ".38 Special").
Many of the .38-200 revolvers produced for Britain were reamed to .38 special and re-imported to the US after the war. You'll note a visible step about 2/3rds of the way down the cylinder - a second one in addition to the one where the case mouth tapers down to the throat.
The bulges that form in a .38-200 chamber will significantly shorten case life as the run expands significantly more each time it is fired and the increased resizing increases the work hardening that occurs.
This is very similar to the issue with .45 Colt brass, as while the .45 Colt is a parallel wall cartridge, the chamber dimensions have .007" of taper in them. This is a throw back to the black powder era to improve extraction in fouled chambers, and for what ever reason the chamber specification has never been changed to reduce the taper. The end result is excessive expansion, and excessive work hardening shortening the reloading life of .45 Colt cases.
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The .38 Special gets work hardened in the middle of the case and that ultimately results in the formation of cracks in the side of the case. The cracks are still in front of the web, so gas loss isn't an issue. I shoot my .38 brass until the cracks appear and then thrown them away. If I happened to miss one and see a crack in a loaded round, I shoot it and then throw the brass away.
If you see me throwing brass into a range bucket, you really don't want to talk it home as it's truly past it's useful life.
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The other thing that people often call a "bulge" is the wasp waist that often results when a sizing die undersizes a straight all pistol case in order to ensure adequate neck tension, usually in semi-auto pistol cases like the 9mm Luger or .45 ACP where the case head spaces on the mouth and thus where a roll crimp cannot be used. It's a purely cosmetic defect, although the increases sizing and the belling then needed to get the bullet to seat cleanly means these cases usually fail due to cracks at the case mouth.
Much like the .38 bass, I'll shoot my 9mm and .45 ACP brass until the mouth cracks.
Below are a series of 1895 Nagant cartridges. It's an odd round where the bullet is seated completely inside the case and the mouth of the case expands to seal against the forcing cone, making it one of the only truly suppressible revolvers. This however requires the case to be able to extend across the cylinder gap on firing. the factor brass uses an hour glass shape to achieve this, while hand loaded cases use an exaggerated roll crimp
Theey are from right to left a factory cartridge, fired case, cartridge reloaded with a factory die set, and a cartridge reloaded using a decapping die, a Lee .32-20 seating die, with a .303 British expander ball to accommodate .313" cast bullets, and then the 7.62 Nagant die with the seating stem removed to post size the round (although partial post-sizing with a .30 carbine die works just as well.
The only purpose was vanity in seeing if I could make a better looking round. The bullet is better centered, but the accuracy of the Nagant pistol isn't good enough for it to ever make a difference.
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Where bulging becomes a problem is when a bullet for what ever reason seats so hard that it bulges or wrinkles the case.
This is distinctly different than the "wasp waist" effect of an overly sized case, as it creates an increase in diameter that will prevent chambering.
This is normally caused by not belling the case sufficiently, to allow the bullet to seat easily. The comparatively thin brass of the .38 Special is prone to this kind of problem, but it normally rears it's had with a case that is too short and gets no belling at the charging die or belling die station.
In general you want to use as little bell as possible to save wear and tear on the case, belling it just the point you can feel the bell and the bullet seats easily.
