Whenever I hear about ants swarming an otherwise live and healthy plant, especially one like bee balm that tends to be insect repellant, I think aphids. The ants would not be attracted to the bee balm, but they are attracted to aphids, which secrete a sweet, sticky substance called honeydew, that the ants love. So check your plant closely, stems and undersides of the leaves.
If you find aphids, your first step is to get rid of them. The simplest way to do that is just to squish them, which they will just sit there and let you do. Or you can spray them with a soapy water solution (being sure it is actual soap, not detergent, which can harm your plants). After that rinse your plants with a hard spray of water to get rid of any remaining ants, aphids, and honeydew.
Then you might want to put some diatomaceous earth down around your plants to help keep the ants from coming back, because sometimes they actually bring the aphids and "farm" them.