Correct link: http://www.seas.ucla.edu/stenstro/Bubble

The source says that this only applies to bubbles >0.1 cm radius.

The source appears to be class notes, and does not cite sources itself. The idea that ascent rate is independent of bubble radius is counterintuitive to me given how Rayleigh drag works (normally appropriate at high Reynolds number). A quick search I did failed to find anything to confirm this. So, I'm leery of accepting this claim uncritically, and I'd like to see a better source here and explanation of the physics.