I have taken both of these tests (the one that Banzai referenced, and the one that odd_one_out referenced); I scored 171/200 on the first, and 39 on the second. These scores seem fairly high.
It is quite probable, though, that the fact that I'm so acutely, insistently introverted led to these high scores. I have only had limited experience with mental health professionals (and they refused to give me any official diagnoses, when I asked, which really confused and hurt me), and it seems their assessment was that I was anxious (socially in particular, but also generally), avoidant and depressed (based on the medications prescribed). No mention was ever made of Asperger's.
The experience you've had with the mental health system is pretty typical. Even if autistic traits are apparent it's common for them to not recognise them for what they are and not make a referral. Many are poor at communicating with the patient about diagnoses and treatments.
Most mental health workers are inadequately informed about autism and this includes psychiatrists. People will accumulate many diagnoses or treatments, often inaccurate or wrong, before they're able to get assessed for autism for which they usually have to fight.
I went through various levels of mental health services and no one ever mentioned autism. When I discovered it I ended the inappropriate (and harmful) therapy I'd been receiving and consulted my doctor who then fought hard to get me assessed (because provision for adults is terrible).
For adults it's tough to obtain a proper assessment and can cost hundreds. Many were already adults when Asperger's was first included in the DSM (I was about 16). For those seeking an assessment it's advisable they consult a specialist in who's experienced in diagnosing adults. General mental health professionals are usually not qualified to make such a diagnosis.