Maybe the reason she has trouble with initiating is that she feels she's not being entirely honest. She doesn't want to convey that she's super horny when she's really just doing it to be nice or loving. I can only be assertive when initiating if I am quite aroused or a little tipsy.
It's much easier for men to initiate. It goes against all cultural training for a woman to have to do it. If you were to go to a bar and start hitting on women, you'd expect or at least be able to deal with a certain level of rejection. If I went to a bar dressed attractively, I'd expect that someone would try to pick me up if I just acted reasonably friendly. Sometimes I have to wonder what stops all of us HD women from doing just that. We must be paragons of moral rectitude. LOLOL
"Tell me, what is it you plan to do with your one wild and precious life?" - Mary Oliver