First of all I think your in a very good position as she was the one who asked you out. She is therefore very much into you and normally its the woman who is looking to push the relationship forward so to speak . IMO its probably a little too early as you need to see how things develop between you both , but the signs are good.

If I was in your position I would be looking at how the land lies a little. For example have you asked about her past relationships ? I am assuming that your partner is roughly at a comparable age so the likelihood is that she has been in long relationships before which would be a god sign . You also need to find out if she is a widow . Its not uncommon in our sort of age group that someone has lost a partner through ill health or tragic circumstances . if this is the case she could and should harbour very strong feelings still for this person and you will need to respect her position here . It is something me and my partner have discussed and both of us would want the other person to find another partner, rather than be lonely .

So you need to find out why she is single ? You can ask that question but fluff it up a bit. For example " I think you are a vey attractive woman , however I am baffled as to why your single? " That way she will open up and tell you about her background and previous relationships.

Another useful probing  question to ask is " Have you got a list of things you want to do in life ?" A relationship may be on that list .

With those type of questions she is most likely want to reciprocate ,so also be prepared for that. We all tend to have baggage from mid life onwards.

So to sum up for now I would just see how the land lies and enjoy each others company and build on that .

Best of luck

That's good.

Enjoy the friendship and company and see how it develops