Bull rush says:
For every 5 by which your attack exceeds your opponent’s CMD you can push the target back an additional 5 feet. You can move with the target if you wish but you must have the available movement to do so.
Does this mean you can start a bull rush, and have them continue moving back, without leaving your starting square?
Does this affect your ability to push a subsequent creature?
The 3.5 bull rush (which behaved entirely differently, even besides CMB/CMD) says
If you beat the defender’s Strength check result, you push him back 5 feet. If you wish to move with the defender, you can push him back an additional 5 feet for each 5 points by which your check result is greater than the defender’s check result. You can’t, however, exceed your normal movement limit.
Clearly you have to move with them here. But the Pathfinder version doesn't make that clear. So, can I send someone flying with a bull rush, while staying put? And if so, does that make Awesome Blow only useful for the fact it does damage?
Awesome Blow also knocks a target prone, unlike Bull Rush. Using it to place a person/creature within a threatened square of something nasty is very tasty.
Yes, PF changed the text of Bull Rush to the point that you can now knock them back without moving at all yourself. Also note that in 3E, moving INTO the foe's space was reqired to start the bull rush. So I liked to think of a bull rush longer than 5 ft being sort of a displacement effect. You move into his square, he's displaced back 5 ft. You move into his square, he's displaced back 5 ft. Ad nauseum. Of course, in reality, up till the end he'd be pushing against you continuously, I just found it easier to conceptualize that way.
PF's completely different. You give a push or whatever, and they go flying back X distance. You can follow after if you want, but that's completely separate from the bull rushing action itself and has no effect on it one way or the other.