Your best bet for finding your way from A to B by bus in Jerusalem and throughout Israel is the travel planner at bus.gov.il. Enter a start point and destination and it will show times, routes and stops on a map.
For a useful overview of the entire public transport network in Jerusalem, you have a choice between an unofficial but regularly updated online map or an official but somewhat out-of-date pdf map.
The first of these, the more up-to-date map of Jerusalem’s current bus routes and light rail line is maintained on a private website: Oren’s Transit Page.
The second option, the only official map currently online (2021) was produced in 2012 by the Jerusalem Transport Master Plan team. It has information and labels in English and includes the network of bus routes in Jerusalem, express bus routes, the light train route, and ‘park and ride’ locations. It’s no longer entirely up-to-date but may provide a helpful overview. Click the thumbnail map above to see the full-size map. It’s a pdf file, which may take a few seconds to open.