I thought I'd throw my two cents in, here. I'm going to use the royal 'we' a lot, so I apologize if this comes across as me speaking for everyone in my same boat.
(Just to qualify myself, here)
I am an MtF Transsexed individual (the term Transsexual/Transsexed denote any individual who actively pursues hormone/surgical treatment) who's been in the process of transitioning since I was 15. I've spent many hours volunteering with LGTBQ+ organizations and getting to know Transmen (FTMs) and Transwomen (MTFs) from a fairly diverse range of age groups, ethnicities, and socioeconomic conditions.
(On topic, now)
While I am breaking my own rule about posting uncited information, I am quite lazy, so here goes!
Studies done in the United States and the Netherlands since the early 1970s to today have found that the neurological behavior of an MtF's brain is generally indistinguishable from the neurological behavior of a natal female (an individual born with ovaries/uterus/the works). The reverse is also true - FtMs show brain activity that is generally indistinguishable from that of a natal male. I won't bore you with the rest of the neural/hormonal response stuff (I'll post a decent resource down below) but what it ends up meaning is that there's a fairly decently documented biological reason we in the trans community end up transitioning - we really are (chromosomes notwithstanding) at least partially legitimately members of the sexes we come to understand ourselves as being.
(This part's a lot more open to interpretation)
It seems to me that if you're finding yourself attracted to a transwoman, you're probably attracted to her feminine qualities. I've had enough people proposition me to infer that it's an easy thing to do! The scientific stuff I posted above would tend to imply that being attracted to her wouldn't qualify you as gay/bisexual on its own merits, as she wasn't really a guy at any point in her life - she just wasn't aware of that fact until she came out/transitioned/what have you. That's not to say that you may not be bisexual, but your attraction to her is essentially a heterosexual act.
On another note, hat's off to everyone who posted something demonstrating tolerance or outright acceptance! The suicide rate among trans people (last time I checked) is still holding at about 30%, so we can use all the tolerance/allies we can get! I'll be mentioning this thread to a few of my other trans friends. I think they'll be as appreciative of your kindness as I am.
And before I forget, if you want to go digging and fact-checking, here's a link to one of the more solid sources of information. In the spirit of fairness, it was written by a transwoman and so should be taken to have a bit of bias behind it. It's also got information that hasn't been kept abreast of newer research, but you all have google, so if you're interested, you won't be left hurting for information.
http://ai.eecs.umich.edu/people/conway/TS/TS.html