If you are staying in Burlington and *really* wanted to take the Vermonter from St. Albans, on a weekday it is possible. You can take the 5:40am or 6:40am St. Albans LINK Bus #96 from downtown Burlington (Cherry St. Terminal) which stops in downtown St. Albans, a short walk from the train station. I did this once when I stayed in Burlington and got to see the train crew prepare and move the train from the yard to the station. I was also the only person who boarded the train at SAB that day, so I had the entire train to myself for the half hour run from SAB-ESX. The bus fare is $4.00 (or $2.75 "step-up" if you connect from a local bus) and takes about an hour from downtown Burlington to St. Albans.
Alternaely of course you can board at Essex Junction, which is reachable Mon-Sat by the Essex Junction #2 bus from downtown Burlington. Mon-Fri you can catch the bus from Essex to Burlington after the northbound train arrives in the evening, but it's not possible (yet!) on weekends, but there CCTA is proposing 7 day service to Essex Jct, including adding later buses to allow connections from the northbound train. The fare is $1.25 and the bus runs every 15-30 mins midday, 30-60 mins later in the evening.
More info on the local bus is available at cctaride.org
Uber is another option in Burlington (a recent addition after being banned from the city), but steer clear of the local cabs especially if you want to make it to the train in time. I waited 2 hours for a cab at the Essex train station one Saturday, when I was told it would be waiting for me when the train arrived, then they wanted nearly $50 for the ride to Burlington. Uber gives an estimate of $21-$29 for the ride.
