I tried using the MBTA's trip planner (
MBTA.com > Official Website for Greater Boston's Public Transportation System), Rider Tools, to plot a trip from the corner of Union Park St & Washington St to the BU East stop. The defaults are minimize transfers, use all services, and walking distance 1/2 mile. That produced two itineraries that look identical to me but are listed at 48 minutes and 55 minutes. Both include an 11-minute walk to the #47 bus, the bus ride, and an 11-minute walk from the bus. The schedule shows the bus running every 20-30 minutes most of the day; less often after 7:30 pm.
The trip planner has produced some extremely wacky trips for people, but this one looks fairly straightforward - at least there are no weird transfers - but I've never ridden that bus, so I can't say how on-time it tends to be or how pleasant/unpleasant it is.
A second itinerary, produced using 'minimize travel time,' has you walking 9 minutes to catch the #9 bus and riding it to Copley on the Green Line, then taking the B Green Line to BU East. That itinerary is timed at 38-39 minutes for a weekday morning. As far as I'm concerned, minimizing your time on a bus is a good thing, but having to transfer is a pain.
Hope this helps some!