In UK (please no Americans unless you lived in UK), if I accidentally bumped a car while leaving a parking space and drove off and the other party

Unless someone is hurt, it's entirely a civil matter over property, so the police will not be involved. The delay for hearing from the other party's insurance company could be fr any number of reasons: no claim has been made; the other party has gone on holiday; they are not insured; the insurance company is just slow. If the repair is expensive, you will hear soon enough.