Hi Jake,
Yep asteroid hunting is a great sub-study in astronomy. A 4" scope could limit what you observe slightly but I observed my first with an old Meade 16XT CCD camera with a cheap 400mm f5.6 camera lens with an objective lens around 65mm I think. In fact I found it and then went looking to identify it.
This article may be of help
http://www.iceinspace.com.au/63-505-0-0-1-0.html
Also hours of reading, don't be put off by the reading OR any talk of huge programs for observation, at this site.
http://www.minorplanetcenter.net/
Good luck and please post any asteroid images in the Solar system section.
