Black beard algae thrives in waters that are nutrient and oxygen rich, and co2 deprived, but are actually pretty uncommon for unplanted tanks. I ended up giving away my plants because they were dying anyway. I stopped adding ferts and I reduced lighting, and then it began to die! Siamese Algae Eaters are the only fish that will eat this algae, but I don't recomend getting the fish just for that. Try turning off the lights for a week, then keep them on for 8 hours per day. Increase water changes to reduce nitrate. If there's no change in a month or so, try making a little DIY CO2 chamber. Most people use them for plants, but it is cheap and easy to make. A really drastic measure is to add copper to the tank, but this should be a LAST resort because copper is dangerous to fish.
There's nothing wrong with bleah! That's actually what you are supposed to be doing. As long as you are rinsing it very well (air drying will help too), then there is no danger