I think that you have laid the groundwork respectfully and perfectly here, and from my perspective personally, you may have likely found one of these.
There is no longer really opprobrium attached to these situations, and I am sure that this lady is very grateful that you did NOT create an awkward situation by approaching her romantically in any way that could be misconstrued by the HR Department, which in Governments, has little enough to do that they will jump all over stuff like that if they sensed an opening.
I know that because I too, took early retirement from the Government around 55, like she has chosen to do.
I remember your story (hazily, at this point) when you told it here before, but not the details, honestly.
You've established the groundwork, she knows you and likes you, so I think you are NOT at all too young to approach the gal; You can reminisce about persons and situations at work when she was there, but you should on this, the third date, get her to talk about everyone's favorite subject - themselves.
It should become crystal clear, as she talks, what her personal dating situation is.
I've done the online dating thing for awhile, and I am 65 years old now, so she would be in the lower levels of acceptable dating range for me, and I know for a fact, that there is a HUGE pool out there of available single females of her age, probably over HALF of every female in the USA 55 or over is unattached AND available for dating.
Show genuine interest about her. Ask about her interests, and her FAMILY; ask how she fills up her days now that she doesn't have to work; ask whether she enjoys life, and whether retirement is what she imagined it would be, making the choice to pull the plug earlier than most folks do; in other words, draw her out, and show real interest in HER.
That will draw out the information you need, but make her more comfortable around you, and view you as a friend, and feel more comfortable and relaxed.
I'd avoid ALL mention at this point, any mention of anything crude, joking or otherwise, of a sexual nature overtly. Women this old have been around long enough to be VERY familiar with those kind of approaches, and I've been told time and again, by them, stories that would amaze and shock you about what men have said to them - and such encounters make them feel like they had just taken a bath in a sewer. But that you probably know.
I'd suspect there is a fairly decent chance you have a pretty good chance for a romantic encounter, here, as women that age have VERY lusty sexual appetites, still, that will absolutely amaze you if you get a good one. And remember also, Frosty, that statistics indicate that the people of EITHER gender that are single at that age, over 50% of them have had NO sexual relations for over a year's time.
Let me say that again: Over a YEAR! That means there is a very good chance she is more than ready -- for YOU!
If you look at the Vodka martini thread, you can see my last girlfriend, who I cut loose right before Christmas, reluctantly but of necessity, I felt after a relationship that lasted near a year. I think all else aside, and so did she, our sexual chemistry was sizzling, the best for both of us, we ever had in our lives. She took me to the moon! Over and over.
She is 63 years old!!!
So yes the hotties ARE out there, and they don't advertise overtly.
VERY good chance you have found one. Judging from your timeline, I think there is a good chance here she likes you and could be MORE than ready.
If it happens though, understand it could easily morph and grow into a relationship, at least in her mind though. Early on, if things go well, you will have that talk - about the ground rules, expectations, and the future. Probably you know that, but I'm just saying. You owe it to one another, as good people.
I wish you well.
edit:
Oh yes, one more thing. On your next meeting with her, bring her some flowers, or even a small book of verse, maybe something like Maria Ranier Rilke, or Khalil Gibran, (for example), had written. That counts as a nice gift and ALL women like that. It is so romantic and they LOVE to be courted. Almost ALWAYS. In fact, I hear that they keep "score".
And the point system is: one point for every gift! Doesn't matter WHAT the gift is, it is the thought. It's the gift, the act of giving, the THOUGHT of them PERSONALLY, that matters and makes them feel special...and makes them feel YOU are special, too....
A new car, a house, a bouquet of fresh flowers, a gourmet truffle in a gift box - ALL equal ONE point.
And they LOVE confidence in a man. I have read and heard that over and over. Enough to believe ALL women adore that trait.
At the end of the 3rd date if it went well, end it with a full-on hug. If it lingers then go for the kiss. lolz