Unfortuantely, no. The A Style and B Style bass bridges are not interchangeable. The A style bridge is designed to have the mount holes under the centerline of each string whereas the B style doesn't follow that convention.
The exception to this rule is the Fender Mount style bridges. Since the A Style and B Style of this line are designed to fit Fender basses, they also are compatible with each other.
However, it can still be messy. For example, the A style FM1 mounts on 3 of the 5 Fender holes whereas the B Style uses all 5 holes. If you had installed an A Style FM1 on a bass without drilling the extra two holes, the B style would have two mount holes unfilled.