Echoing FDO's comment here. Tug boat Master is not a walk on job. You have to train for it and it sure isn't like driving a pleasure boat.
Bosun's used to get a Tender Charge that was essentially a deck hand qualification that, as i recall, was recognized by the CCG. If one could get posted on a tug and got along with the Master, they could (and many did) get hands-on experience running the tug. But, the Bosun never received the full training required to actually become tug masters. They had to do extra schooling on their own time to get their papers. Granted I'm not a bosun, but I haven't heard of too many of them getting posted to a tug in the last decade and a half. These duties have been absorbed by the civilian auxiliaries.
If a tug master is what you want, and you really want to be in the military to do it, go the MARS route. That should take care of most training requirements plus some experience and then all you need to do is challenge whichever test that will give you the papers.
If you don't want the military, CCG college and many marine oriented colleges and universities should be able to hook you up.