I forgot to mention this, but I already took it to a gas station (for the air compressor there) and deflated the tire as much as I could, and then used a screwdriver to push in on the tire near the rim where the bulge was, but when the tire was deflated, the tire seemed to be on the rim just fine. I pushed on it anyway to make sure and didn't appear to be making any difference, so I reinflated it again and the bulge came back just like before.

I actually have been riding the bike and hope I'm not doing any damage. When riding on a smooth surface, I can feel a slight bump everytime the bulge makes contact with the ground as the tire spins. Tonight, I'll deflate again and give it another try. I only have a foot pump at home, so it's a pain to reinflate from scratch, but I guess I'll have to do that.

Is there any chance that my patch caused a problem? Those patches from Walmart were super-cheap, but seemed awfully sticky, giving me confidence that it'll stay stuck on the tire.