After watching the video, I looked at Google Maps typical traffic a bit and was surprised that the Tobin seems to stay green weekday afternoons.
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ftp://ctps.org/pub/Express_Highway_Volumes/01_Route_1_North.pdf has hourly traffic counts for the morning peak from 2007. I was surprised to discover that the peak hour only had 3,600 vehicles crossing the Tobin southbound, which would probably fit just fine into two of the three lanes. A southbound bus lane on the Tobin would change where the queue gets stored, which might slow other traffic to the north which exits onto Route 16 or even further north, but if traffic hasn't increased since 2007, a bus lane on the Tobin Bridge probably wouldn't reduce the number of single occupancy vehicles crossing it.
It appears that if there were a bus route that stopped at the busway's Eastern Ave, Box District, and Bellingham Sq stops, and skipped Market Basket, that the US 1 southbound on ramp at the Arlington St / 5th St intersection would be quite easy for the bus to get to. The reverse direction US 1 to busway route isn't so convenient, and getting from Eastern Ave to the Arlington / 5th intersection involves a certain amount of going north to go south.
If the morning Tobin congestion could be dealt with somehow, I'm wondering if it would make sense to run a one way loop that would start at Haymarket, follow 111's route from Haymarket to the Park St @ Hawthorne St bus stop in Chelsea that both 111 and 112 serve, then travel along Central Ave making at least one of the stops 112 serves, then stop at Eastern Ave, Box District, and Bellingham Sq and continue onto US 1 back to Haymarket. If this is going to be done, it might make sense to start with assigning it four 40' buses during the afternoon peak, if that's successful, expand it to the morning peak, and if that's also successful, expand its hours further. (If it eventually runs 18+ hours a day 7 days a week, I think that might be good, but I also think starting with just the hours most likely to attract strong ridership would be good. And if Boston builds Congress St bus lanes someday, it might also make sense to extend this route to South Station.)