I don’t think a very full bladder would explode. There is a muscle at the base of the bladder which holds urine in and prevents it from leaking out until you go to the toilet. When you go to the toilet, the muscle relaxes to allow the urine to come out. In a very full bladder, the muscle is unable to hold the large volume of urine in the bladder. So what happens is that there will be an overflow and urine will start to leak out, even when you are not in the toilet!
It might feel like it’s about to explode, but as Daphne says, more likely to leak first. I used to work in a lab that did some work with pig bladders (we got them from the abattoirs, so the pigs were already dead for food) – if you clamped the end of those and filled them with artificial urine, there was a pretty decent chance of an explosion.