For some reason, I prefer alder P-basses, even for slap. The last three ash bodied P-basses I've owned (all light weight swamp ash) just didn't work for me, tonally. The claim is that ash is "brighter" than alder, but that did not appear true to me. The ash basses seemed
sweeter in the mids, with less treble (though the difference was subtle...)
Note that ash can vary in weight, from light to heavy and in between. Some believe tone changes along with weight.
Another caveat is that selecting tonewoods isn't like chemistry: there's no guarantee that a bass with body A and fingerboard B will give you tone C: that's because of natural tonal variation within the same species.
Overall, though, differences in tone between woods are pretty slight, in the grand scheme of things. You should check out some of the tone comparison threads. For example in this one, it's hard to tell the difference between ash/rosewood and alder/maple even with high quality headphones: Alder-Rosewood vs Ash-Maple - Alfik response to DanAtkinson experiment