Since they closed the railway station there in 1965, Tregaron has not been the easiest of places to get to by public transport!
The nearest railway station to Tregaron for someone coming from the Warminster direction is at Llanwrtyd, but that is 30 km (19 miles) away, is served by only three trains a day each way, and has, in any case, no public-transport connection that I can find to Tregaron.
A better bet is Carmarthen -- 55 km (34 miles) from Tregaron -- as it has rail connections from Warminster at least hourly, and bus links to Tregaron (though you do have to change at Lampeter). Best of all if you can get someone with a car to meet you in Carmarthen!
Sample journey Warminster to Tregaron:
Warminster d 0739 (train)
Newport a 0925
Newport d 0937 (train)
Carmarthen a 1144
Carmarthen d 1222 (bus)
Lampeter a 1313
Lampeter d 1325 (bus)
Tregaron a 1400