The basic P-90 design was made when most guitars they were being used with had 300k volume pots and 500k tone pots. I don't know about Bare Knuckle specifically, but most pickup manufacturers design their P-90s—humbucker-sized or regular—for the combination of 300k and 500k. Even though most people using humbucker-sized P-90s use them in guitars with all-500k pots these days, that just means those people get a little more brightness, which is likely what they went to P-90s for anyway.
With that in mind, I'd use double 300k pots. You'll be getting very slightly less top-end out of the P-90 than it may have been intended to have, and the bridge and middle pickups will be a touch brighter, but it won't be that severe a change. 500k pots will likely make the bridge and middle pickups very peircing, and 250k pots will probably bring a lot of mud to the P-90; I've never found any P-90 that works out well with 250k pots. You could simply mix a 250k pot and a 500k pot, but then you're giving up some fine control on whichever control gets the 500k pot. 300k pots give almost the same fine control and smooth roll-off as 250k pots, so using both in both positions is what makes sense with this pickup combination, to me.
If it were my own guitar, I'd buy 4-5 300k pots, measure them all and use the brightest ones. CTS have tolerances ranging from 5-10%, Bourns are around 5-7% and Alpha sit in the 10-15% range. Aiming to get pots measuring in the 290-315k range would be a good plan.
Otherwise, I'd use two 500k pots and have the bridge and middle pickups run through a 470k resistor (fixed 500k resistors can be hard to find) before hitting the controls, so the bridge and middle pickups will see a 'full' 250k while the P-90 goes straight through to the 500k controls. The only downsides to this are that it's a little more wiring effort and 500k controls tend to not offer such fine control as 250k or 300k pots. If you leave everything on '10' all the time, no problem; if you do a lot of work with either the volume or tone pots, I believe the 300k option will be much better for you.