In the past I would usually go up to a girl and compliment her, that sends her the signal that you are interested. Try to very gradually befriend her, then work towards romance, but don't ask prematurely and wait a short while (a few weeks). For me, I don't immediately disclose the Asperger's diagnosis to them either.
Also, don't worry too much about rejection, embarrassment, or any of that. Know that everyone feels very nervous but some people hide it better than others. People find others who are cool and accepting of their flaws admirable, and she most likely will as well, because everyone has flaws but some people are more accepting of themselves than others.
I am currently also struggling with this but it's possible to learn how to do it well enough to hide our social ineptitude.