Hi Shifty,
Yes, you should ask her out, even if it has been two weeks since you last saw her.
She was the one who approached you first and then proceeded to approach you throughout that week.
When you approached her as she was talking to her friends, she turned to you and talked to you.
So far, she has shown strong signs of interest.
She wouldn’t have forgotten about you in two weeks.
If anything, she may have been thinking about you quite a bit in these two weeks, perhaps even wondering whether you are thinking about her.
Hence, it is unlikely that she would have lost interest in you.
It is not too early to ask her out.
You are not asking her to be your girlfriend. You are just asking her out on a date.
The sooner you do so, the better.