You've posted on a UK site but there are hints in your post that you're in the USA. (We don't use the hash symbol for 'number', we don't normally use 'thru' and we don't use the spelling 'license' - it's 'licence' here). So the rules in your country might be different to those where most members of this site are located.
However, here in the UK, most people probably wouldn't bother reporting the incident to their insurer (as most policies only require that accidents involving either injury or damage should be reported). Indeed, if every little bump got reported the insurance companies they would probably be overwhelmed with pointless paperwork. (I've had my car bumped in the back by three different London taxi drivers in the space of twenty minutes!).
I'd wait to see if the other driver reports it. (I can't see why they should though).