As mentioned once it's there, it's there for good. Only way you're COMPLETELY eliminating it from your system is a full break down and sterilization of everything. Bubble algae spores are wicked resilient and basically impossible to completely get rid of. There will ALWAYS be SOME bubble hiding somewhere getting a tiny shred of light that will keep the process going.
It's not a death sentence. In a smaller tank it's more annoying. You need to stock up on emerald crabs. They will nibble on it. Urchins will eat it as well
The absolute rock star bubble algae eater though are rabbit fish (foxface). If your tank is big enough (90+ gallons, which some will still say is too small) a single foxface will completely wipe out any visible bubbles within a day or two. Guaranteed. You will still have bubble algae. Look close enough. It'll be growing in dark corners, certain impossible to reach undersides of rocks, inside your overflow, etc. but your visible, attractive, illuminated display will be free of bubbles. They friggin eat it like candy. A word on how resilient it is though, periodically I have to take my durso pipe off and clean out bubble algae from the inside which clogs it. I also have it growing up and out of the water in dry air on my heater power cord. That's right. Just having it be able to touch the water surface it can wick up enough water to maintain a growing population of bubbles in open air.