(Please note: when you choose an answer as a Best Answer, or at least give a thumbs up, it helps those who answer questions here.)
Yes, we have a bus stop with bus service running to Boston and farther down Cape about every hour or more during peak travel times. More info and schedules can be found on the Plymouth and Brockton (bus company) website.
That is about as good as it gets for public transportation on Cape Cod. I have many friends in the area who take the bus daily from Sagamore Beach and work in Boston.
Below is a link to other means of transportation for Sagamore Beach and the Bourne area.
There is also taxi services as well. You can google Sagamore Beach transportation.