Bulge in barrel: looking down a very clean bore, you might see a slightly dark ring at the bulge. On the outside, you may be able to see it when sighting down an octagon or round barrel, tapered barrel is another issue.
A tight fitting cleaning patch will slip easily throught that area, then continue with whatever pressure you previously applied.
Safe: if it looks like the python that swallowed the pig, I'd say no. A bulge of a few thousands likely is OK, but I'd hate explaining how it got there to others, especially if it was your fault.
Accuracy: some have said a small bulge (whatever "small" is) did not degrade accuracy, others disagree. I bulged a 1858 Rem barrel, my own fault, shot it about 20 times more and didn't seem to affect accuracy.
Couldn't stand to look at it so replaced, and BTW, not an impossible task, even with a few simple tools like a vise, a very big crescent wrench, and leather vise jaw faces, a file, and feeler gauge for cylinder/barrel clearance, as a factory replacement barrel may already have the front sight installed, so you need to screw the barrel tight into the frame with the front sight "up."
The beauty of ML shooting is that, unless you are a world-class champion shooter, many ML firearms are forgiving and many are not dramatically affected by reasonable loading variables.