In reply to higherclimbingwales:
Bothy is around the same altitude as the base of the amphitheatre but in the next valley branch over, so you have to either go :
(1) a long way around (basically via the Eigiau carpark so you could leave gear/supplies there) around 8km with an easy loss and then gain of 100m or else
(2) go up the path to Melynllyn then over the top of the ridge (Gledrffordd) - as short as 3km but a (steeper and pathless) height gain + loss of 250m.
Post edited at 18:09