Leaving a bore sighter in place usually bulges the barrel worse than that, even splits it, you got off easy.
I don't worry about it somehow damaging the rest of the barrel or the action.
I would:
1. Test fire. If it retains "hunting accuracy," great. Carry on.
2. If not, I would look at repairs. Cutting the barrel off behind the bulge would work, but would lose the front sight. Replacing or reinstalling it would be added work. I would ask my gunsmith about counterboring the barrel a few inches. This is said to be pretty common on Mosin Nagants, it ought to work as well on an American rifle as a Russian. Appearance would be unaffected and velocity only a bit lower.
3. Replace the barrel. Haunting the sale sites for the same roll marks might take a while and cost a bit, but it is certainly possible. Of course a new barrel from a blank could be in any caliber that would fit the action and and might well be more accurate than factory.
I once had a similar experience. I bought a rifle at a gun show. I wondered why somebody would put a gun up for sale without cleaning it, but the external appearance was good and the price was very good.
Accuracy "off the table" was poor. The first cleaning, I felt the patch "jump". Yup, a bulge.
It was near enough the muzzle to cut it off and stay legal, so I had it done.
Accuracy was only somewhat better, so I got it very clean and examined it very closely. The proverbial "dark grooves, good lands" of the surplus rifle salesman. But this wasn't a surplus rifle, it was a Remington 788 .223. I didn't know anybody made corrosive .223, but it sure looked like a previous owner had found some.
Remington said they would rebarrel it for a reasonable fee, so I sent it in. I just sent the barreled action so they would not have a chance to mess up the nicely refinished and checkered stock. When it came back, it did not fit the stock well. Different serial number; Remington had not rebarrelled it, they had simply replaced it. Whole spare barreled action on the shelf years after the model had been discontinued. I had the stock rebidded and finally got my bolt action .223 but with a lot more cost and delay than I liked.