pjp is fan to the unnecessary double post, coupled with unnecessarily tall signature.
anywho...
rex, though i sympathize, i can't fault the cops here.
the waiting period is set up by design. imagine how many reports there'd be of stolen property if those it was missing from weren't even entirely sure it was stolen! say your little brother lent your playstation to a buddy of his. or your stolen wallet ends up being found back at work where you left it. or, in this case, say your aunt came over to borrow the bike, but no one was around to tell.
stuff like that happens all the time, and the waiting period is set up to help avoid confusing a real crime with a perceived crime.
unfortunately, there are only so many cops, and they don't know you or your situation well enough to be able to instantly judge if you're 1000% sure or 1000% crazy.
the cops driving around doing nothing could also be doing a lot more than you think. yeah, we've all seen cops loafing around or stopping for donuts or whatever -- but thats not an aspect limited to cops; look at construction workers and lifeguards and waitresses and the president and yourself. but, in this specific case, you don't know if they were really lazing around or actually on a patrol of sorts.
what i can agree with you on is someone acting rudely while your mother explains herself in person or on the phone. though there's certainly an explanation, there's simply no excuse for that, and its a trait unfortuantely all too common for various receptionists.