There are a few unique considerations here, most of which I'm sure you are already aware of. And these considerations are specifically geared toward the early phase of counseling when trying to establish a bond with the client.
It has been my experience that people with an autism spectrum disorder dislike talking about themselves in general. However, they do enjoy talking about their special interests. Your client no doubt has a preferred activity. So initially, instead of directing questions to your client in an attempt to get her to talk about herself, identify her special interest and let the conversation revolve around that.
Once you have identified her main interest, spend a little bit of time researching that activity so that the two of you can exchange ideas about it. Here you are making statements about the special activity based on your new knowledge of it rather than asking questions. (Although a few related questions sprinkled here and there may be beneficial.)
Individuals with the disorder also are out of touch with how they feel. But they do like to talk about facts, especially those associated with their preferred activity. Thus, in the early going of therapy, it may be helpful to talk about facts associated with your client's special interest, and stay away from questions and comments about feelings.
I believe it is also important to match the eye contact style of the client. As I'm sure you know, individuals on the autism spectrum do not make a lot of eye contact because they do not glean information from facial cues and other body language. So if your client is looking down for example, you may want to look down at a notepad on your lap periodically, followed by a few seconds of actual eye contact.
Also, people on the spectrum are easily over-stimulated by a series of questions, both emotionally and cognitively, which often results in a shutdown. This may explain why your client doesn't answer your questions or simply says, "I don't know."
Lastly, I would keep sessions short - no more than 15-20 minutes initially. This will help avoid over-stimulation and a subsequent shutdown. Also, the ideas above are strictly for the "bonding phase" of therapy, and can be used for 3-4 sessions before moving on to the more serious stuff.
* The Aspergers Comprehensive Handbook is an easy-to-use guide which gives you, the parent, the simple yet highly effective tips, strategies and techniques to help you cope with and manage your child’s behavioral and emotional needs.