While the job of the Bos'ns is probably the closest that the Navy gets to Infanteers, the bulk of their responsibilities lies in other areas.
Bos'ns will be the ones who close up on the 50 cal machine guns when needed, such as when there is a threat of fast incoming attack craft. Now-a-days, the Navy trains for these scenarios to prevent incidences such as the bombing of the USS Cole in 2000.
Bos'ns are also responsible for the maintenance of all small arms aboard the ship, ranging from the aforementioned 50 cals, the 9mm Sig Sauer pistols, shotguns used by the boarding party, C7s, and others that I can't quite recall at this moment.
As for a small arms specialist, the closest that the Navy really gets to that would be becoming a member of the ship's boarding party. The boarding party is open to members of any trade. Bos'ns are a part of every boarding party, as they are needed to, at the very least, drive the boats.
The bulk of a Bos'ns responsibility lies in the area of seamanship. When coming alongside, receiving a fuel line from one of the tankers, or pretty much any task that involves the ship's lines, the Bos'ns will be the ones on site directing the majority of the activity. (Note they are not "In charge" of these evolutions, that typically lies with the Commanding Officer, or his delegate.) This is the prime place where the comparison between Bos'ns and Infanteers are made. Bos'ns have the most physically demanding job in the Navy. While they're not as liable to have their knees destroyed, they're the ones who'll spend their days on the upper decks, lugging lines, or driving around the ship's boats. It is a demanding job, but again, many do find it rewarding.