Concord Coach runs bus service from Boston South Station and Logan Airport to Bangor. I think that it runs through Portsmouth rather than Manchester in NH. So, you might do better flying into Logan rather than MHT. That said, I don't know how late the last bus leaves. You may still need to stay overnight at the airport and get a bus in the morning. If you fly into MHT, I think there is a shuttle service of some sort that will get you from MHT to Portsmouth. Maybe someone on the Forum here knows more specifics about that.
A Concord Coach connection by way of Portsmouth, NH is not a possibility. Concord's latest published schedules show no service to or stops in Portsmouth... they just don't provide service there. Their schedules also show no late-night-early-morning service from Manchester to Boston, so you'd likely need to spend the night in Manchester, take one of their morning runs to Boston and catch the bus to Bangor from there. Not particularly appealing as an option, but you may decide it's worrth a second look once you get an estimate for limo service... Some of the limo services serving Manchester Airport include a "cost estimating" function on their websites so that may give us some idea...
A reality of life in northern New England is that, except for a few major cities, public transportation of any sort (cabs, bus, limo, etc) is infrequent-to-non-existent. And where it does exist, it can be more expensive than expected because of the long geographic distances and sparse populations (meaniing less demand for servicee).
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