I can't identify the moss species for you. That would probably require a bryologist? (moss expert)
I can tell you that it appears to be a normal moss that is suitable for bonsai. I believe the tall stalks are called seta and have a capsule (sporangium) at the tip which will mature and open to release millions of spores that may go on to grow into new mosses. Mosses do not actually flower but in essence your moss is preparing to breed.
If you don't like the look just trim the tall bits with your shears - mow the lawn.