Bergamot will spread--it grows wild here in fields and seems to thrive in the sandy soils here. The lavender one is probably a cultivar of our lavender Wild Bergamot (Monarda fistulosa) and the red a cultivar of our wild Bee Balm (Monarda didyma). But it's not that vigorous a self-sower in my experience--it spreads more readily by rhizome, instead. So if I want to contain it in an area, I just contain the roots with some sort of barrier.
Not sure what it might do in your neck of the woods, though. Is there some place to check to see if it's considered invasive in your area?
"We are--each of us--dying; it's how we live in the meantime that makes the difference."
"It's not what you gather, but what you scatter that tells what kind of life you have lived!"
"Be kinder than necessary, for everyone you meet is fighting some kind of battle."