Bump didn't use direct device-to-device communication. A central server correlated the two bumping phones, based on geolocation and accelerometer data, then swapped the data via the server. At least that's how it worked in the early days. (Wiki page confirms)

Since it's relying on your internet connection, skeptical it'd be faster than AirDrop for a large amount of data like photos. But for swapping contacts I bet it was faster since it didn't have to spend time establishing a new direct connection.