the bull rush attack is a special attack action, which has as an effect of the attack, movement. as the ability states, you are trading damage for forced movement. it is not a move action, nor a move equivalent action. there is nothing prohibiting a move action before a bull rush, or after a bull rush. the only possible point of contention between a bull-rush and a move action is the clause in bull-rush where it says you can't exceed your normal movement rate - which could be interpreted as intransitive (ie: only affecting movement within the bull rush action) or transitive (ie: affecting all movement you take that round, thus if you seriously bull rush someone, you could potentially run out of movement in a given round).
the dm would be well within rights to interpret it either way, but to fully prohibit movement in a round where a bull rush has taken place is not what the rule says.
Also, there is no touch attack. (is the dm thinking of grappling instead?) the attacker provokes (or not depending on feat choice), there is an opposed str check, and then adjudicate the results. period.
generally speaking, if a dm wants to change how it works "to make more sense" then said dm needs to do so in a way that reduces complexity, or adds an amount of complexity acceptable to all group members, and notify all players of such alterations before the game / campaign even starts - as it will affect character choices. imposing sudden limitations on character concepts, especially those previously approved is simple bad form. a dm is not the absolute authority of a group (only over characters inside the context of the game), and must get approval from an entire group before making any such rules changes.
by making these last points, i do not seek to state or imply that you dm is actually doing any of it. but it is an important concept to keep in mind for all dms, so i state what might be considered obvious to many, just in case it is relevant and/or useful.