ID'ing SW algae is tricky, at best, without having a microscopic picture, checking cell structure, ect, but I am going to guess it IS a Caulerpa species and I am going to take a chance that it is C. racemosa . A bit different than the one I posted earlier but it is the same genus.
The common name "Bubble algae" is Valonia species that has no runners or holdfasts visible, but just has little "bubbles" that attach to rock, pumps, tubing, ect and can get very invasive. It does have predators, though.
I do not consider it a nuisance in a main display. I think it has nice, unusual texture that can enhance a aquascape. I don't know if I would use it as a sole plant, though. It is cool but....
Some consider any Caulerpa species undesirable because of their tendency to grow fast, use up the available nutrients and sporulate. When they do, they release toxins and nutrients into a closed system that may not be able to biologically deal with a sudden increase in nutrients.
I find the benefits of these alga species outweigh the risks. Having them in a main display, where we can visualize them, it is possible to tell when they are becoming depleted of their nutrients (basically nitrate, phosphate and iron) and will begin to realize their existence is threatened. Their growth rates will significantly slow. That stage does go for a while, so the hobbyists has time to correct the issue. If the alga is hidden in a sump, the aquarist might not notice until it is too late and the alga has gone into "help the species survive by making spores until conditions are better" mode. I even notice that an alga will have one frond turn white and then I have a day or so to harvest big.
The benefits in a small tank would be a major biological filtration system that will allow you to safely have more fish and feed them like they need to be fed. It sucks up nitrate and phosphate like no other techinique or gadget we have available and all it costs to run is a bit of harvesting now and then.
Or, you can get rid of this algae and trade it in for hair algae or cyanobacteria?
OOPS! I typed the sentence " I do not consider it to be a nuisance" right after I commented about Valonia. It might sound like I do not consider bubble alga to be a nuisance.
Actually, even though I do think it has a place in our hobby, I do consider that Valonia can be a PIA in a system without a rabbitfish!
I do not consider "grape" alga a nuisance. It is so easy to harvest, you just reach in a pull a handful of DOC/nitrates/phosphates out of your system. Nutrients in-nutrients out. Easy.