feinting doesn't have much to do with BAB.--wrong.
Um, actually, I was right about that. About 14 years ago, I took a fencing class and in one afternoon I learned how to feint. That's all it took. One afternoon. My BAB didn't go up that day. I don't remember leveling up either. I learned other ways to feint later on, but feinting doesn't have anything to do with how well you can handle a weapon.
If I stab low at your leg, you either lower your guard to match that (thus being suckered by the feint) or you realize that you leg is already guarded and an attack there wouldn't inhibit your ability to fight so you keep your guard up (and are not suckered into the feint).
Of course, some feints are almost guaranteed to work regardless of skill. If I stab at your face, you either raise your guard high or you turn away or back away. Even if you know tactically that your face is safe, there is a primal fear everyone has of seeing sharp metal coming right at their face and the urge to block that or move out of the way is nearly impossible to resist.
I stand by my method:
Bluff (for rogues, bards and sorcerers), Concentration or Intimidate for everyone else. Opposed by Concentration or Intimidate, or maybe Sense Motive for those that have that as a class skill. Circumstance bonus goes to the person with the highest BAB.
THAT is simple, and reliable. Easy to remember. Easy to execute.
I would also change the mechanic slightly and treat it as a move action when used in conjunction with a standard attack action. Or I would allow it to be used in place of an attack when someone is making a full round attack action and has at least 2 attacks.
I wouldn't tie Improved Feint to Combat Expertise or require a 13 Int and I would allow it to provide a +4 bonus to Feint checks, both to make the feint and resist it.
While you're at it, you could allow the option to do an extra 1d6 damage on an attack following a successful feint OR have the target flat footed for the next attack. This makes feinting a lot more useful especially to those with high BAB who otherwise would have little or no reason to feint.