i own an aerodyne
the top of the body is carved. something like the old les paul basses.
the bridge sits in a cavity, because the top is carved. you need to change it with something that fits. i changed mine to a hipshot vintage, which is actually smaller (shorter) than the cavity.
if you take out the aerodyne pickguard (assuming yours is an aerodyne with a pickguard) you will discover that it is just an ordinary 11-hole jazz pickguard. i replaced mine to a tort pickguard which i bought from frenchtoast who i think bought it from basspartsresource.
the holes will line up but the part of the pickguard adjacent to the control plate will not. what i did was i filed away the pickguard at that part so that there would be more room for the control plate. problem solved.
it is common for pickguards not to line up perfectly with fender basses, nothing to do with it being an aerodyne or whatever. at least i didn't really have to 'massage' the holes, which happens sometimes. if you've ever changed a pickguard you would know. use common sense, when you buy a pickguard, bring the original pickguard and try to get a best fit. that's what i did, and it still wasn't a perfect fit.