The concern would be for the bubble coral, not the other way around. :) Clowns are usually very aggressive with what they are hosting and can easily kill LPS corals such as bubble corals, frogspawns, hammers, etc. if they decide to host them -- especially if the coral is small relative to the fish's size. They basically beat the polyps to death, forcing them to stay retracted all the time, so the coral dies.
The coral can sting the clowns, but the worst that will result in is some discoloration of the fish.
Some good alternatives to anemones that clowns seem to take a liking to that can hold up to the clowns are xenia, toadstool leathers, and my clowns' favorite, hairy mushrooms.