Driving, flying, bus ?? Driving will be easiest in terms of being able to set your own schedule,
Bus would require your taking a bus to Boston and transferring there to a separate bus to Montpelier.
Not sure which would be less expensive because I don't know how you value your time.... doubt that bus or air would reallly save you a lot of time over driving once you factor in waiting times at terminals, airport security etc...
For exact schedule fares and options, I'd suggest you check the websites for Greyhound Bus Lines, and the Bangor or Montpelier Airports..... or the Flight section here on Trip Advisor.
Driving routes -- define "best way" : most scenic, shortest, fastest, least fuel consumption, avoiding tolls, backroads, highway, or other?
US Route 2 is probably the most scenic and shortest route, despite all the twists and turns and small towns (288 miles, 5:48). Parts of it just seem take forever, though. Depending on how you drive (and traffic conditions), it is possible that I-95 south to Hampton, then NH101 west to Manchester, I-93 north to Concord,then I-89 north to Burlington could potentially be faster. It's 100 miles longer, and google maps says 35 minutes longer, but if you're a lead foot or just prefer interstate, it could be a wash time-wise; of course there are a lot more tolls, too.
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