Sure. Bass handle aquaria fine so long as their dietary requirements are met (>40% protein <10% lipid feed and/or live minnows) and the water is kept clean, a kiddie pool should be no different. I'd study up on solids filters, biological filters, and UV sterilizer recirculation systems to ensure long-term success (some literature here:
https://srac.tamu.edu/categories/view/24).
You can also physically dig a small pond basin and line it with plastic pond liner (rigged with the same filters mentioned above). This would look a little nicer since you could shape the edges how you like. Or just make a basin the kiddie pool will fit in and be done with it. If you're really wanting to get creative, you can build up your filter plumbing to discharge above the pool, then arrange some decorative rock around the discharge pipe to conceal it, then epoxy or grout, whatever, the rocks into place so that you make a cool little water fall into the pool (good for oxygenation and de-gassing along with aesthetics).
You'll likely need to scrub the sides every once and a while to keep algae down but the filters and UV sterilizer will help keep this down a bit.
Bass will standout badly over a blue kiddie pool background and shallow clear water; birds may become a problem that might require net or wire mesh covering to solve. Bass are jumpers too; the pool will need to be covered if it is elevated off of the ground at all.
