I was First Lieutenant on two of the cutters I served on, and as such was in charge of the Deck Department. Boatswain's mates from E-4 to E-7 were in my department, but the bulk of the department was E-2 and E-3 guys. Mind you, my cutters had total crews of around 75 to 100; on larger Coast Guard and most Navy ships, the "deck crew" s a division of the Weapons Department instead of a department.
There is also a warrant officer and chief warrant officer level of boatswains, "Warrant Boatswain" and "Chief Warrant Boatswain" -- typically referred to to as "Bos'n." These come fromt the ranks of enlisted Boatswain's Mates who pass a rigorous warrant officer exam and have the other time in service and command recommendations.
There are many, many Boatswain's Mates in the Coast Guard, given the number of boats (vessels up to 65 feet long) and ships operated by the service. Many are cross trained as maritime law enforcement officers (though this is now also a separate enlisted rating), so they are involved in boardings at sea. They also, in the senior enlisted ranks, serve as officers in charge (the enlisted equivalent of Commanding Officer) of small cutters and, ashore, boat stations.
Boatswain's Mates have a reputation of being rough, tough, sailors, and many of them embrace that. I have known many Boatswain's Mates, though, who were among the best and most effective leaders of any of the ratings, and being "rough and tough" wasn't the way they got to where they were: they were highly intelligent, dedicated, and good with people.
Any Boatswain's Mate E-4 to E-6, call 'em "Boats" as a sort of nickname (like "Guns" for gunner's mates and "Sparks" for radiomen). Any E-7 and above is always, always, "Chief." And a Warrant Bos'n is "Mister".