Bus

Note that The Aberfoyle Coach company is no longer operating as of July 2012.

The First No. 10/310/C10/C12 service runs between Glasgow and Balfron/Drymen and calls at Strathblane.

The First No. 515/516 service runs between Balfron and Strathblane.

The First No. 512 service runs via Carbeth to and from Balfron. It is primarily for school children and only runs on school days and at the start and end of the school day.

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.
There is also a joined up timetable with bus/train connections during rush hour.
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

The Strathblane area is readily accessible by car and is not far from Glasgow. A map of the area can be found here