“What do you do?” is a perfectly reasonable question. Work occupies a great deal of our lives. It can reveal what interests someone, what she knows, and what she has spent years learning.
The conversation becomes narrow when it never leaves that territory.
You exchange the names of companies, discover a mutual contact, and describe what you’re working on. You like her. Then the evening ends, and you leave with a clear account of her responsibilities but little sense of what spending time together might be like.
Another question could take the conversation somewhere else.
What has she been reading? Has she lived here long? What does she do when she has an entirely free Saturday?
There is no need to conduct an interview. Offer something of your own. Mention the class you tried, the film you disagreed with, or the place you keep returning to. Let a conversation develop around something you both find interesting.
Sometimes it will. Sometimes you will have a pleasant exchange and move on.
When you do want to see someone again, it helps to be specific. “We should get together” is easy to agree with and easy to lose. “Would you like to see that exhibition next Saturday?” gives the idea a shape.
She may be busy. You may discover that your schedules are difficult to reconcile. Making friends as an adult involves practical inconveniences that chemistry does not automatically solve.
Still, an invitation is a beginning.
You do not have to know whether this person will become a close friend. You only need to know that you enjoyed the conversation enough to continue it.