I think you might be conflating Logan Express, the suburban bus service that runs out to lots around 128, and the Back Bay Express that runs free in one direction to Copley Square. I believe it's $3-5 on the return. Haven't taken it but seems to run frequently; I see them on Boylston street regularly. Buses are clean and new. Of course, it's subject to the same traffic peculiarities as any other vehicle.

For what it's worth, I took the silver line yesterday to south station, which is also free. You can move to a train or subway from there. It is one stop to back bay on the commuter rail on many trains out of South station and you won't need a ticket for the three minute ride (just make sure you don't get on a train that goes to Middleboro or Plymouth).

Uber/Lyft I find annoying at Logan because you have to schlep to central parking for pickup. Also, anecdotally late night arrivals typically come with sparse options and surge prices. I don't mind taxis these days; they seem to have gotten cleaner and competitively priced with ride shares.

For context, I live in the city and used Logan about 35 times last year.