Fastest, and generally easiest, way to get from Logan to Bar Harbor will be:
-- Logan to I-95 North (your car rental folks will have directions for that)
-- I-95 North through New Hampshire into Maine, and north to I-305 in Bangor, ME
This segment will involve one toll booth in New Hampshire ($2.00 toll) and Maine Turnpike toll plazas at York ($3.00), New Gloucester ($2.25) and West Gardiner ($1.75) The Maine Turnpike pre-dates the Interstate Highway System and was designated I-95 when Maine developed its Interstate system and was allowed to retain its toll system on its portion of the Interstate.
-- I-396 from Bangor to US Rt 1A in Brewer (I-395 begins at I-95 and ends at US Rt 1A, so not much chance of getting lost here).
-- US Rt 1A from Brewer to US Rt 1/ME Rt 3 in Ellsworth.
-- ME Rt 3 from Ellsworth to Bar Harbor.
Usual travel time is between four and three-quarters and five hours not counting stops....
You may get suggestions that you get off I-95 in South Portland and use I-295 from South Portland to West Gardiner. Doing that would save you a little in tolls, but in our experience will usually take longer than stayiing on I-95 because it runs through, instead of around, downtown Portland; involves more traffic congestion between Portland and Brunswick than you'll find on I-95; and has on-ramp and off-ramp slow-downs and congestion issues we don't find on I-95 because I-295 has many more exits than I-95.
No guarantee you won't hit construction along the way -- it is summertime in New England after all... In addition to possible short-term repaving projects, you can expect to hit a short one-lane section on I-95 in Fairfield, ME (just north of Waterville) due to an ongoing, long-term bridge repair project.... in general, this porject has resulted in speed reductions, but few stop-and-go situations. When you see the advisory signs, move into whichever lane is remaning open well ahead of time and watch for the reduced speed signs (Maine State Police do enforce Work Zone Speed Limits and fines for speeding in work zones are automatically double the usual amount).
In general, Maine DOT orders contractors to open as many lanes as possible and cease all on-site work by noontime on the day before major holidays; if that continues to be their policy, I'd expect little to no actual construction work in progress by the time you get into Maine. And absent a major crash of some kind, slowing down and working your way through any lane restrictions will still be quicker than trying to find alternate routes in unfamiliar territory.