The ASD child is cut off from the world in an informational sense: in what they hear, see, and feel and in what we ask from them.
Understand the various approaches
While potty training a neurotypical child, we sit them on the toilet and we ask them to do what they have to do. Soon enough, they will make the connection between the discomfort of needing to go and the relief of using the toilet. For an ASD child, the connection is not so natural. They will learn by heart that they must go every time their mother asks them to or rings a bell, before every meal or at any other moment that they decide to link with using the toilet. The association will be made with an external reference.
However, if this reference is absent, so is their cleanliness. They will not realize, by themselves, that their bladder is full, that they are uncomfortable. They don't understand that by using the toilet, they will feel better. As long as we did not teach them visually the link between what goes on in their body and sitting on the toilet to pee, they will not understand the meaning of this action. We must always keep in mind that what is obvious for us is not necessarily obvious for a person with ASD. Never take for granted that they understood what you expect of them.
At home and elsewhere
It is not uncommon to see a child with ASD being clean at home but refusing to use someone else’s toilet. Another concept that does not come naturally is generalization. This concept must be taught with visual support. Do not think that the person knows that they can relieve themselves anywhere besides their own house, that toilets can have different shapes, different sizes, that there are various types of bathrooms (private and public), etc.
Also, they may not be able to use a public bathroom because of overstimulation: the toilet flushing by itself, the dryer, many people talking, etc. It could be because of hypersensitivity to noise, because they fear the moment when the toilet will flush or when the dryer will start because they don’t understand what it is there for.
Listening for success
You have to listen; the slightest little thing can make everything change. When you are dealing with an ASD child, you must remember that he is cut off from the sense of information. The information that exists in your head is not the same that is in front of him. The sense (color, smell, size, noise, etc.) doesn’t correspond to what he knows. The information is new. He is not trying to manipulate, to make fun or to oppose you. He probably doesn’t understand what you expect of him and why he should do it.