Busses to and from hikes

Hi,
We plan on hiking from thingvellir to Hveravellir via Hagavatn in June or July. What would be the best way to get to thingvellir from Reykjavík. And is it possible to take a bus from Hveravellir back to Reykjavík via Gullfoss and Geysir. By bus we mean the cheapest option and not "tourbusses" or is this the only way?

Thanks in advance and we hope somebody can help us out...

There is in general no distinction between the tour bus and (longer distance) service buses in Iceland.

Bus timetables here. http://www.nat.is/travelguideeng/bus_stop_the_real_icelandic_old.htm

Kynnisferdir bus to Thingvellir from Reykjavik BSI daily at 0830, but arrive in good time to get your ticket and seat as lots of things leave at 0830 and its the same bus as the popular Golden Circle tour. http://www.nat.is/travelguide/bus_schedule_thingvellir_geysir.htm

There's also a TREX bus at 11.00. http://www.nat.is/travelguideeng/bus_stop_laugarvatn_gullfoss_geysir.htm

Kjolur bus to Reykjavik leaves Hveravellir daily at 1200, but will give you only 20mins each at Gullfoss and Geysir. http://www.nat.is/travelguideeng/bus_stop_reykjavik_kjolur.htm

Thanks, we'll check those websites out!