There are two sets of public toilets within the building. One is between the two sets of entrance doors, as you enter, the ladies is to your right and the gents to your left. Each of these includes a disabled person's toilet.
The second set is in the cafe area. Continue (west) passing the stairs to your right and an entrance to the staff area. The first opening leads to the ladies (in front of you, after turning right), whilst the second opening (at the west end) leads to the gents, turn right then go through the second door on your left.
More information and further links can be found on the Access Guide to Burrell Collection page
Background information on this pilot project is available on the Access Guides page