It is walkable, but there are also free shuttle buses (the “Blue Bus”) in almost constant motion between the two schools. According to the posted schedule, the buses take 10 minutes campus-to-campus, and there are about 34 runs from each campus on weekdays. At peak times, there is little wait; for example, there are five scheduled runs from BMC to Haverford on Monday mornings between 10:05 and 11:05 am.
Getting to Swarthmore or Penn requires more planning. There are shuttles to Swarthmore, but they take longer and are less frequent. For Penn, I think you have to take the train.