Tire with a bubble on the side - is it safe to keep driving?

A tire with a bulge on the sidewall is a serious risk because that area gets more pressure during turns and can burst suddenly. Best thing is to change the tire before you drive, especially if you're hitting the road.

It's not safe, full stop. A bulge on the sidewall is exactly what you don't want to have because the pressure there is higher when you're cornering or braking hard. The tire can blow without warning, and if that happens at high speed it gets ugly.

Change the tire before you leave the house. It's not a question of "maybe it'll last longer," it's really about avoiding trouble. If it's a new tire and the bulge is small, you might be able to just swap the tire at a quick mechanic, but if it's already worn, better take the chance to put on two or four new ones, depends on what makes sense for your wallet.

Go straight to the tire shop, get the tire replaced and that's it. I had a car with a bulge on the sidewall a few months back, I ignored it because I thought it was nothing, and then it actually burst on a curve in the rain and it was way too intense - ever since then I don't take chances with that kind of stuff.