Here http://www.streetmap.co.uk/streetmap.dll?G2M?X=541236&Y=197188&A=Y&Z=1 is the Robin Hood pub, which is near the heart of the forest so may be a good place to start from - it should be on bus routes. It's also near the Iron Age fort at Loughton Camp, which among other things is thought to be the location of Dick Turpin's hideout.

See also the official City of London Epping Forest site at http://www.cityoflondon.gov.uk/Corporation/living_environment/open_spaces/epping_forest.htm