Conclude the conversation like you are working on an informal letter, just make it something interesting and fun it with a smile.
You can say something good like, “I have to be going now, but I’d like us to extend our friendship and see you again so let me call you.” Without the phone number, you will never get anywhere with a lady. Because to create a meaningful thing, you will need to set a date.
To set a date, you will need her contact. Just take some steps forward as if you really want to take your leave and turn back to ask politely by saying “kindly dial your phone number because I can’t sleep a day without hearing your sweet voice”, and smile while handing her your phone.