The most up-to-date pdf public transport map for Reykjavik, Iceland is a schematic map. If you prefer a topographic map, which makes it easier to see real locations, click the map image below (Opens a pdf in a new window). Then zoom in to find the routes you need.
Information is in both Icelandic and English.
When you’ve figured out which bus line you want, you can find timetables for each line on this Icelandic bus company’s timetable page