Why not allow bonus attacks from natural BAB to be used for move actions and immediate actions and some standard actions.
A fighter with 6/1 could sacrifice the +1 attack to intimidate an opponent.
A fighter with 15/10/5 could sacrifice the +10 attack to take an additional five foot step.
With actions being among the most valuable currencies in D&D... why not use BAB in the same vein as you do caster level and translate them to bonus actions.
There are other additional things you could do.
For example you could "Ready a block", doing so would sacrifice your attack with the lowest BAB, but in doing so once per round you would gain that BAB as a shield bonus to AC or a reflex save against a single attack.
A fighter with 6/1 could sacrifice the +1 attack to intimidate an opponent.
A fighter with 15/10/5 could sacrifice the +10 attack to take an additional five foot step.
With actions being among the most valuable currencies in D&D... why not use BAB in the same vein as you do caster level and translate them to bonus actions.
There are other additional things you could do.
For example you could "Ready a block", doing so would sacrifice your attack with the lowest BAB, but in doing so once per round you would gain that BAB as a shield bonus to AC or a reflex save against a single attack.