See if you can remove the bubbles w/o breaking it. You might have to rock it gently back and forth but they can come off in a ball.
If one breaks take a new toothbrush and scrub the affected area real good. I would also setup like 3 or 4 other cups with your saltwater in it and dip the coral and swish it, move to the next cup, dip and swish, etc... then put it in the tank. Really get it rinsed well.
Bubble algae is what caused me to bleach half of my liverock, couldn't get rid of it otherwise. It doesn't harm anything just a pain. I also didn't want to get an Emerald crab which eats bubble algae because I guess they can be hit or miss with it (but mainly hit).
Just my advice.