Although you are allowed to take your bicycle on the BTS Skytrain for free, the MRT Subway only allows foldable bikes. But not just any foldable bike as it has to be smaller than a certain size. Here is a picture posted by Davina Kunvipusilkul on Facebook which gives the details:
Foldable bicycles on the MRT should not exceed the following measurements: 1140mm x 640mm x 360mm.
The dotted yellow line on the poster is actual size to make it easier to check.