Persistent manual removal of the algae, along with using emerald crabs is about the only thing that works. Foxface rabbit fish will eat a little of it also. Buy emerald crabs with red color in their joints. These will (should) pick and eat smaller bubble algae.
I got so frustrated with bubble algae that I did an experiment. I set up a 10 gallon tank with nothing in it and used a ton of carbon in the filter. The water I used contained undetectable levels of nitrate, silicate, and phosphate. I let the tank run for several months until it cycled and everything that tried to grow in it was dead. I changed the carbon, then placed a rock with mushrooms, anthellia, and bubble algae on it into the tank. I left the light off for more than a month until the mushrooms and anthellia was bleached and practically dead. The bubble algae was as alive and green as ever....no sign of die off or stress. They didn't seem to grow at all though. None of them burst either.
If it is not dealt with, bubble algae can ruin a persons reef keeping joy.