I do find this one of the more difficult aspects of knowing how to act with my AS friend. Often if I feel that I have been asking for too much time or contact, I will ease up and wait to hear from him, so as to give him space. I often will say 'oh, if you feel like company, let me know'. Then I may eventually hear from him, and he may start talking about how bored he is (or has been) and how he has nothing to do, and I get frustrated thinking 'welll... I did say if you wanted to do something, let me know, maybe you just don't want to hang out with me'. A few times, I have come outright and asked 'welllll why didn't you suggest meeting up' and I get the response 'oh it didn't occur to me to ask, even though I do/did want to meet up'! or 'oh, if you wanted to do something, you should have said'!.
So sometimes, I don't know if to just keep asking, or to just ease off and think 'well if he REALLY wants to meet up, he'll let me know'!