While it's very nice and caring of you to be so willing to look after this boy with zero advance notice when his caregivers flake out - and yes, they are flaking out -- it does nothing to get these parents to step up and give their child reliable pickups. Saying you want to give them your new number, etc. is basically enabling them to be flaky about this, and I think you would do them and the boy more good to say "I like your son and have been glad to help, but you do need to have someone else pick him up because I cannot guarantee that whenever he gets of the bus and no one's there, I can take him home with me that day or even walk him to the house." Surely your own son has activities and places he needs to be at times? You're being very nice and mellow about this which is great but...it's enabling them to be too casual about their own kid.
One day you are going to have other plans, or pick your son up early from school by car to head to an appointment or event, and no one will be there for this kid, and if he does get home on his own, he might find no one there, or dad so asleep he doesn't come to the door. It doesn't sound like a family that's awful or abusive, just one where the adults are not on top of the fact they have a kid who is new to school, new to buses every day and on top of it has Asperger's which could make it more complex.
Does dad work nights? Because it sounds like that might be the case if he's asleep in the middle of the afternoon. Mom needs to phone him from her own workplace every day at the same time to get him up and out the door to meet their son. Suggest it nicely.
Others have posted "why can't the kid walk home alone" but if he's in K that may not be good for him. Someone also said your son should be walking home on his own, but you should not have to give up that daily walk with your son - that's a time when kids often talk about their day with their parents. You should be able to meet your own kid at the bus stop if you want and not be always wondering if this is a day you have to worry about this little boy, or a day you can carry on with other plans you had. I'm not being hard-hearted about the boy; I think the parents need to get better organized about pickups. They may need you to say no every time in order for them to get the message clearly. They've come to assume that SOMEONE will help him if he's not picked up by dad or this other person.
And yes, find a way to talk to the bus driver and ask the driver to alert the school that the boy is not consistently met at the stop. Some schools actually have rules that someone must meet kindergarteners at their bus stop on their return home, so the family may be breaking a rule they don't know about.