I was thinking about how I would use it. It would be a multi-classed character, where i stopped at a partial level. Never again to gain any more points in that class. I would like to see it be a one time feat - you can take only once. But it would round you up to the next BAB if you need less then 1.
I appreciate the feedback; it's helpful when trying to flesh these things out. I thought about a one-time feat, but then it becomes way underpowered. I was comparing it to "An Axe to Protect Me" which brings a Dwarven Wizard to the average BAB and "An Axe to Save Me" which brings them to good BAB. I realize it's a racial feat, but still, we're talking two feats that transform a Wizard into a full caster, with all bonus Metamagic feats in tact, as well as a full Fighter. Granted, it's only with an axe, but nonetheless devastating.
The spirit of this feat is significantly watered down intentionally in order to represent additional combat training while still maintaining class progression in an alternate path. Hence why it's only .25 fractional BAB. Think of something like a Bardic Paladin. A follower of Melodi that starts off as a Bard, takes this feat at 1st level to go from .75 BAB to +1 BAB, then cross-classes to a Paladin at 2nd for a total of +2 BAB. If they choose to continue with these two classes or experiment with others, such as Asinjin's many characters, they have the option at feat gaining levels to choose to take something different, or perhaps stack another instance of this feat on to represent their pursuit of fighting skills without having to take a class in Fighter.
I feel that being able to take it once only benefits someone wanting to take a single level in a .75 BAB class like Bard, Cleric, or Rogue then never touch another class that isn't a full +1 BAB. It's too limiting. The ability to stack at least gives people a fighting chance to gain an additional BAB at higher levels, so it gets incrementally better the more you take it, thus scaling with higher level characters. For example, someone who decides to go full Rogue takes this feat four times over the course of 20 levels. By the time they reach 20th, they'll have four base attacks at +16/11/6/1 instead of three attacks at +15/10/5. It isn't a big increase, but enough to represent their dedication to combat training and reward them with an extra attack. Again, high level pay off with the long game in mind.
With all that being said, it could maybe be increased to a .5 fractional BAB and limited to only taking twice or something like that. That way no character could ever gain more than a +1 total BAB over time. I'm open to suggestions, so keep them coming.