No ^,^What happened for me was that it slowly stopped over a couple months. Then for a month I didn't really have a sex drive. Now I'm 'active' maybe once a week but don't have to act on it. It changes from person to person but it doesn't go away. Figure I went from being active every day to a couple times a week. It's not a huge difference but it's still obvious ^,^
But sex doesn't disgust you or anything? The nature of it just changes? Honestly, I could deal with (even appreciate) a reduction or change in the nature of her libido, but I don't know if I could continue dating her if HRT turned her asexual, so that's the important distinction.
Basically as for my understanding of hormones (I have very little ) The sex hormones like Testosterone and Estrogen regulate your sex drive. When a trans woman takes a medication that inhibits the Testosterone production that will lower her sex drive and without taking Estrogen can stop it all together. Once she starts taking Estrogen her sex drive will normalize after a while because your body has to adjust to it. Hormone Replacement Therapy is a big thing for your body to go through so it takes time. If I'm wrong someone can correct me ^,^ but it shouldn't make her asexual.
I'm 6.5 months on hrt. I have little to no sex drive and am not sexually attracted to anyone at this time, at all. I feel like it's mostly just a phase right now. If I had someone who enjoyed being with me and helped me be comfortable with my body, then I don't think it would be difficult to get in the mood. My body issues can be a pretty big mental block. Hormones effect everyone differently. The major thing to realize is that her masculine libido, that hungry horny drive to get it on all the time, more than likely will disappear completely. Learning to develop and embrace a more feminine libido is a process and takes time. YMMV
I'm not MTF, but coming from the other side, I will say that HRT did make me feel more comfortable in my own body. So, while your date may not have that "masculine libido, that hungry horny drive to get it on all the time" as DhammaGamer put it, many trans people actually feel less disgusted by sex/their bodies while on HRT. How that affects your date, if it does, I can't say.
its different for everyone. people can be asexual, "homosexual", "heterosexual", pansexual, bisexual before or after in any combination - its different for everyone for me when i started HRT, my sex drive changed kind of quickly my desire for intimate relationships didn't decrease, just shifted what i wanted out of them ejaculation is pointless most of the time, stimulation isn't do get horny, just differently also have little to no control over my genitals my sexual preference went from heterosexual male, to probably heterosexual female (still in transition so can't say for sure, just what I'm seeing) - kinsey 1-2 maybe so you will probably still have a sexual relationship, just be open to change in it ^.^
I was sexually very active. Started Cyproteron+Systen patches in May 2014. I peaked sexually late 2014 mostly bi with a strong preference for men. Then I met someone trans who dumped me in the most horrific manner possible. After that I have had zero interest in sex, intimacy, relationships, love, et.al. The idea positively revolts me and it has for close to one year now. I prefer this nuisance does not come back. I will be having GRS in one month, and I am seriously entertaining the option of having only a vagina cosmetically - i.e. no inside vagina and no sensitivity in the clitoral area.