I had a feral that lived in my hay barn for 6 years. He was, of course, not neutered nor had he apparently had any shots. Once I knew, about a year after he came, that he was staying I started to feed him in hopes of making friends. I could not trap him, he was too smart. Over the years he got more beat up, probably made hundreds of kittens, got sick and seemed to be dying several times. I still fed him but he would not let me near him.
2 years ago I started trying again to get closer. I would do my chores with the horses and just walk around him but not changing where I was going. I guess at that point he figured out I was just going to walk by him so he stopped running off when I got close. One day while walking by I stopped and bent over and held my hand out about 3 feet from him. He rolled over and I knew I had him. It took a year after that. He made the moves, I just squatted down and put out my hand and he eventually learned that head rubs were his favorite thing. He is on the couch next to me now. Still very odd, my other cats are not crazy about him but they tolerate each other.
I have had much easier times, usually with kittens, but have learned over the years with all the odd assortment of cats that show up here on the farm that none of them are remotely the same. Your situation sounds like it will resolve fairly quickly since you have a cat who is attentive enough to have gotten her in the house.
Time and patience. I would get so tired of squatting and holding out my hand that I thought I would pass out but it worked. The fact that you get her into your lap is really good. She will learn quickly I bet.
Bless you for tolerating the fleas. That is rough. Have fun, sounds like you are totally in love with her already 
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