The marines obviously knew Bishop well, but from the way Burke put it, he made it sound like Bishop was assigned to the ship, and not necessarily the marines.
I was thinking that another good question would be if the marines of the 2/9th were assigned to the Sulaco or rotated ship-to-ship during each deployment, like modern marines, but the lockers and other personal touches in the ship seem to suggest it's they're permanent station. Same with the dropship, but it's possible that they could've loaded all of that stuff and got set up prior to leaving Gateway.