Tough one beesimo - I hate looking people in the eye, opticians visits are a nightmare.
I'm not autistic officially but do have dyspraxia, was told I was borderline ASD, I wasn't diagnosed with it as I have developed reasonable communication skills and my Dr felt the diagnosis wouldn't help as I already had the dyspraxia dx which does also cover some social issues. They went with dyspraxia with strong atutistic traits or something along those lines.
It's hard to describe what it's like, for me society is baffling, I 'get' some stuff, like asking people how they are etc but not other things. I often get in hot water due to saying/doing the wrong thing. I'm often criticised for not agreeing with everyone else and stating an alternative opinion, but you could just call that assertive. My behaviour is inconsistent, one day I'll be very chatty and chirpy, the next I won't talk, I don't really understand it myself. I often do/say stuff to DP and get a baffling reaction, he's beginning to realise that sometimes I am genuinely bewildered by his response and not meaning to be rude.
If your colleague does have Autism or SN chances are she's struggling to 'get' social norms. What are her specific issues other than getting on with people? Does she struggle to remember instructions? Is she disorganised? Does she take compliments well, if you praise her work is she receptive or does she not seem to care? If the latter she could be struggling with self esteem.
Some issues can be worked around, I find when I've been trying to befriend others on the spectrum a softly softly approach works. I did work experience once with a lad who I think had reasonably severe Autism, he also had Tourettes. He didn't want to socialise much, I just remained light and friendly 'do you want to come to lunch with us? no? ok, no worries, we're at Costa if you fancy joining later'. He never did come to lunch but over time he opened up and started talking more and interacting with us more as a group - he even started volunteering to present towards the end. I think the last thing you should do is pile pressure on her, as in if she doesn't want to mix just say 'ok, let us know if you change your mind' rather than being visibly annoyed so to speak.
I wouldn't say anything to her yet, if her Mum is concerned she may be on the spectrum it may sound better from her? Hope that helps, you could try contacting an organisation like Remploy who help disabled people in the workplace - they could probably advise you on best practice on approaching a potential difficulty with an employee you think may be caused by a disability.