It is probably simple incompetence along with the understandable reluctance of police to ruffle powerful feathers. There was no evidence of foul play, the D.C. police were pressured into the search by national conservative outrage, so their heart wasn't in it, so to speak. It wasn't as if it was their job on the line, after all.
My vote is for simple incompetence along with bureaucratic inertia. Remember, this is the D.C. police force!
Anyone who would have kept the body hidden for some time would NOT have dumped her Sony Walkman with her weeks after Why not? plenty of killers keep souveniers, maybe this one chickened out about keeping the walkman and dumped it.
I do think it was a murder though...