I lived about a mile away from that location for over a decade but never took Logan Express from Back Bay; I got to the airport by taking taxis and then rideshares when that became a thing. But if it helps, I did take Logan Express from Framingham (30 miles west of Boston) quite a few times and they kept extra busses and drivers on hand so they would always leave on time, but I-90 traffic through Boston would delay the journey to BOS by 30-45 minutes during rush hour. I would guess the busses from Back Bay wouldn't hit most of that traffic because they don't get on I-90 until after the I-93 junction, but could still get delayed by 15 minutes during the worst traffic.

As for tickets, if you want to use a debit/credit card, you should purchase on-line in advance. IIRC (and it's been a number of years, so this may have changed), if you buy a ticket from the driver on the bus, it's cash only.