Couple of options: Sullivan Sq and Bunker Hill on Orange line. Also Bus 93 goes from Sullivan station via Navy yard.
Thereâ€™s a free shuttle from Navy yard MGH to downtown Boston. Also water taxi from Navy yard to Aquarium that cost just $1.75.
Yes the Bunker Hill stop on the Orange Line is on the edge of Charlestown. There's also great bus service throughout the neighborhood that can connect you to other lines. And many people walk to downtown/financial district from the neighborhood. I have many clients who live in Charlestown and love it, so happy to help!