I want to ask a single mum out but we haven't even spoken? advice plz!?

I basically know this single mum, but not personally because I have never spoken to her, but I would like to get to know her, but how do I know that she isn't dating someone else?? All I know is that she is a single mum, but I haven't a clue as to whether she is dating someone or not! I'm quite shy and I don't want to look like an idiot by asking her out and then she says "No Sorry i'm already seeing someone" That's the last thing I want is to look lke a fool, but I am attracted to her and i haven't a cluw how she feels about me because we haven't even spoke, but we see each other once every week because we do a course together and in same cl, but we don't always sit next to each other because she starts the cl a little bit later than me, so she will sit wherever she wants.