I happen to know one of the customs and immigration staff at the Seletar Airport terminal. I saw him recently and he complained about some cyclists washing their bikes inside the public toilet and making quite a mess of it. Its happened regurarly enough that the entire immigration department and the cleaners there are seeing red.
They are asking for this nonsense of a habit to stop. I say they are right. The public toilet is meant for you. It is not meant for your bicycle. Please wash your bikes at home in your own toilet. If you drive and worry about dirtying your car, then please ride to the ride.