An additional complication not touched in the existing answers is the disparity in number of passengers that can be handled by an airliner and a bus.
A large bus might be able to accomodate somewhere on the order of 50-100 passengers comfortably while maintaining a reasonable turning radius and maneuverability as well as reasonable boarding and unboarding times, assuming luggage remains handled separately.
Large aircraft can handle far more passengers than that. For example, an Airbus A380 can take 853 passengers, and a Boeing 767 can accomodate up to 375 persons. Even the MD-80 can seat up to 172 passengers.
This means that you would need anywhere between four and seventeen bus roundtrips to get everybody onto the plane (two for a big bus and a MD-80), as opposed to simply moving everybody through a single jet bridge at the gate. Intuitively, this would seem to take far longer, in turn reducing aircraft turnaround and thus driving costs up. While the time to board passengers can still be used productively, I find it doubtful that the same could be said if the time to board passengers was at least several times longer.
For aircraft up to the number of passengers that can comfortably be accomodated by a single bus roundtrip, other issues (security, etc.) notwithstanding, boarding by bus remains a possibility without significantly impacting turnaround. But those types of aircraft tend to not be used for anything but short haul flights anyway.