You can transplant it anytime. It's so invasive, it's hard to kill it.

Most plants transplant best when they are not actively growing, ie in either the spring or fall. You can try now but it will need coddling and watering.

you can do it now if you need to- just trim off the flowers, so that the plant's energy goes back to the plant, and not to flower production.

bee balm's sturdy stuff, and as long as you keep in hydrated, it should be fine. I like to dig the hole to recieve the plant first, and fill it with water, then I dig up the plant while that's soaking in, divide it as needed, make any soil amendments (adding compost to the hole) and plop the plant in to the muck in the bottom of the new hole (if there's still standing water, you have clay soil, and may want to add two handfulls of fine mulch, and a cup or so of sand to the mix to start breaking it up)

try and have the 'crown' (the place where the plant emerges from the earth) at the same level it was growing, then
backfill, water, mulch.