I'd agree with the others, but I'd go further, plants are the answer and you just need to increase the plant mass. I like a few floating plants, these have the advantage of being easy to thin, and flexible in allowing you to control the light reaching the submerged plants.Plants and algae compete for the same nutrients so introducing fast growing plants may help, it is not the answer...
Never kept these, but I do have Red Ramshorn snails, and these eat BBA when it is young, but aren't very useful when it is older. Red Ramshorns are fairly plant safe, but you need to make sure you get these and not the "Columbian Ramshorn" snail, as that is a plant eater.Crossocheilus are reputed to eat it.
I don't like using chemicals like bleach and excel, but they would give you a quick fix. Personally I'd add Ramshorm snails and some floaters, either those that "wet-handed" suggested, or Water Lettuce (Pistia), Floating Fern (Salvinia) or Amazon Frogbit (Limnobium), and then wait. Over-time the old BBA will be shed, the older leaves will die off, and the new leaves will be kept BBA free by the snails.
cheers Darrel