"Powerhouse" is a funny metaphor, but what else can you say about a bridge that still has four subway tracks crossing it? The Manhattan Bridge not only carries the B,D,N and Q trains, but it's also a major truck route from Brooklyn, Staten Island and even New Jersey to Manhattan - and to New Jersey.
There is one path on either side of the bridge. They were both closed during World War II, to prevent spying on the Brooklyn Navy Yard, but somehow the City never got around to reopening them afterward. In the 1980s the bridge was discovered to be deficient, which meant that the subways on both sides were closed for several years. Then the north side (Sixth Avenue) was closed, and then the south side (Broadway). The paths were used as staging areas for the subway reconstruction, so the city did not make them available until 2001. The south/west path is intended primarily for pedestrians, and the north/east path primarily for cyclists.
In 2007, the DOT restricted a single lane to high-occupancy vehicles inbound from 6-10AM weekdays; it's not clear how much of an effect this has had on congestion or bus movements. The only city bus to cross the bridge is the B51, but there are several private buses that use it, primarily serving Chinese and Orthodox Jewish communities.
On the Brooklyn side, much of the traffic congestion on Flatbush Avenue can be blamed on merges for the Manhattan Bridge. It would make sense for buses to have an exclusive route through Downtown Brooklyn, either on Flatbush or on Flushing or Park Avenue.
Much of what I wrote about the Manhattan side of the Brooklyn Bridge applies to the Manhattan Bridge, with the main difference being that the Manhattan Bridge points people towards Midtown instead of Downtown. Through-running between Brooklyn and New Jersey would be easy because it's a straight shot across Canal Street (and wasn't there some DOT plan to make Canal Street one-way eastbound?), but you'd have to have a bunch of people who either (a) want to go from Brooklyn to Jersey or (b) want to get off along Canal Street and change to the subway, since there aren't too many destinations along Canal.
People from Brooklyn that aren't going to Lower Manhattan are more likely to be going to Midtown, so the best solution would be to hook up Manhattan Bridge buses to a north-south busway in Manhattan, such as the planned First/Second Avenue BRT.