Could I date a mature student?

I am a lecturer at a University in the UK, male, 46 years old and single. I mostly supervise post graduate students such as those working on postgraduate research. My colleague supervises a young woman of 34 who I do deal with at times but I am not her thesis supervisor. I am very attracted to her and we often socialise in the same group and I have developed rather strong feelings for her, now I've found plenty of students attractive but none so much as her and I've never before felt so strongly that I was prepared to risk so much to see if she might like me also. I am not good at reading the signs women send out so I'm not sure that she does like me that way but she does certainly seem to like me as a friend. How can I take things further with her and is it okay for my to date a mature student who is not directly a student of mine?