There are spores in the bubbles. But there's a very low chance that popping them will lead to new growth, and not trying to remove them is guaranteed to lead to new growth.
It is a myth to say that popping the bubbles guarantees spreading the algae.
"Much has been said about the danger of liberating spores when popping the vesicles of bubble algae. This is particularly true for members of Order Valoniaceae, but even then,
the vesicles are said to be a sporulant risk only when having reached at least a third of their full size. Even if spores escape when you botch the job of vesicle-removal ('vesectomy', anyone?), those escapee spores have to run the gauntlet of herbivorous filter feeders, filtration equipment, and the wild lottery of hitting a good, unoccupied spot to settle and grow. Those spores will eventually be released anyway if you don't remove the vesicles."
Horge Cortes-Jorge Jr., "'Bubble' Algae: Selected Descriptions, Controls and Comments."
http://reefkeeping.com/issues/2002-02/hcj/feature/