Pole mzee maka.
Clearly, you have feelings for the lady. She feels the same about you. No one wants to admit it.
The lady wants you to make the first move because you are the man. And the society expects(requires) men to test the waters first.
The lady is playing mind games with you. You have to pull a fast one on her. I'm not a don Juan, but I know a simple plan that works on almost every lady. It borrows from the concept of using money to make more money. Similarly, use women to get women.
Make sure you meet your "lady friend" with a very hot chic. Make some positive comments to the hot chic in front of the lady friend. You can even coach the hot chic on how to play along once you meet the lady friend. See if she gets jealous.
If your lady friend has feelings for you, she'll definitely be jealous. This is your turn. She'll be vulnerable, and will most likely play nice to you. Unleash your game plan to get laid with her ASAP.
By the way, hope she's not a Wazualet. If she is, she must be smiling.
Live Full Die Empty - Les Brown.