My tank ran for about
20 years without a hint of bubble algae until one dang mushroom frag I added that must have had spores (
did not have any visible bubble algae) buried in the piece of rock it came on... within about two months of adding, I started seeing little green balls everywhere...
Admittedly, it was a FOWLR tank for ten of those years, but still... bubble algae sux!
Btw... you might have some type of Caulerpa macro (rather than bubble algae), since you say it had a small stem. Bubble algae will grow in a cluster of bubbles, Caulerpa will grow in a string or line/row of bubbles, somewhat looking like grapes.