Dumbrock Muir is just across Craigallian Road from the North & East Car Parks. To make this walk more interesting and increase the distance a tad, we shall go a more difficult route.
Whatever Car Park you have parked in, make your way to Mugdock Castle and then take the path down Mugdock Wood. When you reach the West Highland Way, turn right then walk to you come to Craigallian Road, cross and rejoin the West Highland Way.
When you reach Carbeth Loch, make an about turn climb over the stile and make your way back through the forest path. At the path junction go left. This will take you down the Cuilt Brae Road.
After you pass the Farm House on your right, you will reach a gate across the road, there is a small grass footpath on the right, go down this then turn left and walk until the path crosses the burn.
At the top of this path go right then left and this is where you join the Dumbrock Muir. If you do not have a Map of the area look for the Pylons, one of them is in the forest to your right; the one to its left is close to the North Car Park of Mugdock.

The ground can be a bit boggy on the Muir at times, but it is a pleasant walk on a good day and the views are excellent.