Bus

The First No. 8/C8 service runs between Glasgow and Balfron/Drymen and calls at Strathblane and Carbeth.
In addition to this, Aberfoyle Coaches run a C8 service which calls at Carbeth with some more useful times

The First No. 11A service has a couple of Sunday services which might be useful

Train

You can also get a train to the nearby town of Milngavie and then get a taxi or bus from there.
Train times from Glasgow city centre can be found here.
You can then call a taxi from the station (Please use one of the local businesses) or ask for directions to the Milngavie taxi office - a short walk away.
Both of the First bus services call at Milngavie Station.

Car