If a character has both of these feats, I would assume it works this way:
The character makes a shield bash, which triggers a free bull rush. The attack is rolled normally, but to confirm the bull rush, add 2 to the result (from Improved Bull Rush). Then, the victim of the bull rush provokes an AoO (from Greater Bull Rush), allowing the attacker to get in another hit. Does that look right? I think my fighter will be headed for this feat mix, and that sounds pretty cool. Also, would the free bull rush from Shield Slam cause the attacker to provoke an AoO if he didn't have Improved Bull Rush? I'd assume not, but I just want to be clear.
Looks right to me. Shield Slam doesn't provoke.
I suggest 2 levels of ranger (weapon and shield style) and get Shield Slam faster that way.