I'm surprised at what basses I do better with... Since it doesnt sound like you have much experience going out and trying different basses may not help you.... but it very will might, so go out and start trying a few basses. Check out the string width at the bridge and up at the nut... The string width, height of the strings off the body top can make a big difference too. Of all my basses, my old Ibanez Roadster is the easiest to pop/slap. It has a bolt on neck and a lot of space between the strings and body.. so my fingers never get caught hitting the body.
Others probably have great options too.. practice and make sure you have enough space between the strings to easily get your finger between so you can grab and snap the strings easily. My basses with tight string spacing I jsut can't do it well... But that may just be me.