There are several bases for the Borders hills . One is Moffat

Buses to Moffat from Edinburgh here

Buses to Moffat from Glasgow here

However, none of the three Borders corbetts have buses to their startand hitchhiking will be required along the Moffat to Selkirk road

Peebles is another base , and useful for several smaller hills . It is reachable from Edinburgh.

A useful bus servive runs from Peebles to Biggar giving access to hills including several DonaldsĀ  from Drumelzier

Timetable here