How to date an independent woman?

Well if she does like you she is scared to admit that she may need you and if she is with you all the time it will feel like she has to rely on someone else for support. This makes her feel out of control. It sounds like she just wants some space to be able to think. When you mainly rely on yourself to support yourself it is really hard to change and let another person control your life in a way. Try to be a bit less clingy: maybe to remind her what life was without you. Sounds like she may be bored but i don't know maybe try to surprise her more often.