An urchin and a few emerald crabs should handle that problem. I had a waay worse case in my lower tank and small two tuxedos and about 5 crabs now keeps it under control, looking right now the only bubble algae I see is on one of the urchins.
You can kill it all now and but you'll probably get it again with a new coral.
Also bleach?? I think fresh water will kill it.