The root of BBA (Audouinella spp., and occasionally Rhodochorton spp.) is always carbon. Red algaes, like BBA and Staghorn (Compospogon caeruleus and Batrachospermaceae spp.) thrive in moderate CO₂ and high Dissolved Organic Compounds (DOCs, note that "organic"=carbon-based in chemistry… technically that’s an oversimplification, but it’s close enough for our discussion). DOCs are a rather metabolically expensive carbon source, so plants usually leave them alone. When you're supporting a vast, complicated vascular structure, it's better to optimize for the more efficient inorganic carbon. Algaes, on the other hand, are just trying to make a single copy of themselves before they die. If they do that, then they're successful, and anything extra is a bonus, so it's worth the extra effort for them to utilize organic carbon.
So, buildup of organic waste is a common BBA trigger. That's why the first places you often see it are on driftwood, coarse/dirty substrates, filter sponges, and filter outputs (since dirty filters are a huge source or DOCs). High or low flow/surface agitation can result in fluctuating CO₂ levels as well, which can be a trigger. CO₂ injection that isn't optimized properly can do it too.
If vacuuming is done frequently, then it's not an issue, but when a large amount of detritus is allowed to accumulate (especially in coarse gravel) then a gravel vacuum can kick up as much as it removes. It can also relocate a lot of detritus to the filter, so that the filter output is then spewing invisible DOCs into the tank, feeding the BBA.
Finally, BBA has a knack for snowballing when it attacks plants. When plants adjust to a drastic change in nutrients, light, etc. they actually reprogram their DNA, leaking waste proteins and other DOCs out of the leaf margins. That's why you often see BBA preferentially attaching itself to the edges of leaves. Well, if it's able to attach to any part of the leaf, it smothers that part, causing the leaf to try and adapt to a new lower-light environment, feeding the algae, and making the problem worse. Eventually, the leaf will usually melt entirely. For that reason, once it's established on a leaf, the best fix is usually to trim that leaf. Sometimes you can pluck it off. Sometimes you can spot-dose with something like Excel, H₂O₂, APT Fix, or APT Fix Lite. For Anubias, I've had luck with removing the plant and dipping it to kill the algae. But of course, the root issue still needs to be solved.
For a large outbreak, this is what I'd do:
1) clean the filter
2) start doing weekly 50-75% water changes, with deep gravel vacuuming each time
3) trim all of the affected lower leaves from the stem plants. Leave some at the top to support the plant while it grows new leaves. Once it has good new growth, trim the tops, discard the bottoms, and replant the tops.
4) for slow growing plants like Anubias, I would do a bleach dip:
Two bowls large enough to fit the whole plant, 50% bleach/water mix in one, in the other, water with 1-3 tablespoons of powdered dechlorinator (like Seachem Safe). The powdered dechlorinator is important, a tablespoon of that is enough to treat 3,600 gallons of tapwater. You just can't get that kind of potency with a liquid dechlorinator. You literally "dip" the plant, like 1 second, in the bleach bowl, then straight into the dechlorination bowl and let it sit there for 15 mins or so. Then put it back. The BBA will turn white and die off. The higher concentration with the shorter duration actually makes this a more effective, and yet gentler treatment than lower bleach percentages, which require longer dwell times to be effective.
5) scrub any driftwood and rocks with a toothbrush. Submersible electric ones work best, but any toothbrush works. If your driftwood is getting soft, then it’s decaying rapidly. In woodworking we describe that wood as being “punky” and it’s indicative of advanced rot deep inside the wood. I recommend removing any punky wood, there’s just no good way to keep BBA off of it.
Here's an example to help you identify Black Beard Algae.