Look around the Los Angeles Bike Coalition page: http://labikecoalition.org/

They work with local political agencies. Especially look for the links about the Los Angeles Department of Transportation. LA DOT actually have a bicycle advisory committee and a Bicycle Coordinator: http://labikecoalition.org/positions/bac_vacancies.html

Also, what about local trasportation agencies (e.g. Los Angeles Metro)? I'm sure there are lots of public policy fights about bikes on public transit, bike lanes, etc. Do a little googling and I bet you'll find alot.

Good luck!