I'm a female-to-male, but I can say that many people feel VERY scared about telling ANYONE. Even if they're not scared to tell you, they might be scared of something else that's hard to explain. When you're transgender you're usually extremely depressed (even if it doesn't show). Depression causes a lot of irrational fear, and intensifies your normal fears. I've known multiple people who really wanted to transition but were too scared to even look up any info about how you actually begin the process.
I met my wife online and knew her for three years before we ever met in person, and soon after we started dating. For those three years I had thought she was a guy because she refused to tell me her gender (and hadn't ever corrected me). So I was really surprised when we met of course, but that didn't change anything about how we were friends. I like her so much that I assume I'd still have been willing to try dating her even if she had been male - since her looks and gender isn't the reason why I like her, it's her personality. Your general personality doesn't change after you transition, but I think you normally become a better person because you're much happier. For example, I help out around the house more, I eat better, I'm much less grouchy, but I'm still me.
My wife says "I don't think about your body, I just think about the fact that it's YOU" so the transition doesn't bother her in that way. Probably someone who met in person from the beginning and always had a fixed idea of what someone looked/sounded like has a harder time, I don't know.
When I told my family it was because I had already started the therapy process and had been living as a male for a year. I thought I could hide it until after I had started hormones, but I could no longer stand it that they called me "she" and so on. It felt like a knife to the gut every time. It got so bad (because I was so depressed), that I felt "do they want me to kill myself?" and at that point I had to just tell them, otherwise perhaps I really would have killed myself.
In fact there was no reason for me to hide it, really. They had never been against gay people, and they knew/assumed that I was gay. My mom was pretty sexist and also tried to put me in a dress a few times, but I lived with my dad so the situation wasn't all that bad. But it was like my brain had decided "this is how things have always been; they've always called me female" and I was deadly scared about the whole thing because it would disrupt what was "normal" for us. The specific topic of what they thought about ->-bleeped-<- had never come up and that's where the fear stemmed from.
I had seen how people treated stuff like male-to-female crossdressers on TV that aired where I lived - they were always ugly and were essentially just a joke. That was all I knew of transgender people (since they never appeared in books) until I began researching myself, and that was how I assumed my parents thought of transgender people. Actually, in the end I was right to hide it for as long as I could from them but I won't go into that here lol!
Some transgender people who want kids desperately want to transition before their kid is old enough to be able to remember them as the wrong gender.
As for talking or not talking to your partner about it... I remember that when I was telling my father, I had so much pent-up emotion and I was so depressed that I just said some really weird things. The further I got into my transition (especially after I had my first chest surgery) the more sympathetic I became to other people and the more emotional feelings I got when GLBT topics came up. As in nowdays if someone talks about growing up as transgender on TV I actually end up crying. I also end up crying at stuff talking about the end of adolescence, probably since that's when I realized I was transgender and realized "ah, THAT'S my problem" and nowadays I feel sort of like I "missed out" on my entire childhood or something. Me crying would have been unheard of before, so you should prepare for possible weird stuff like that I guess...
I think it helps to go out and read/watch media with transgender stuff in it, you can do it together if you'd like. I tend to do this with my wife, then she can ask me "Is it really like that? I don't get it at all" and I can say yes or no. In the meantime, I feel like I don't have to give her a big speech or anything because we can both "experience" things through the movie.
If you want some fiction recommendations and don't already know about these, "Hourou Musuko" is a comic about both a boy who wants to be a girl and a girl who wants to be a boy (the boy-to-girl is the main character), it shows them beginning to realize their feelings in elementary school and follows them all the way until the start of university. Out of everything that I've ever read and watched I think this is the thing that has treated ->-bleeped-<- the most nicely and realistically. The part about simply wanting to transition but all of society being so against it is the biggest thing.
"Peacock" is a movie about a guy who dresses up as a woman for half the day or so - having to hide that he does this from the whole town. It slowly grows into more and more of the time that he's dressed up (if I recall). I won't say more and spoil it. It's not specifically about ->-bleeped-<-, but the guy is really good at acting the female part, and it's not one of those American movies where you're supposed to just laugh at the guy in a dress. The part about "hiding" things is the biggest theme.
"Cockpit" is the only other one I remember right now, where a guy starts living as a woman because he can't get a job as a man. It's a sort of feminist comedy as I remember and the ending gets kinda crazy, but it's okay. Since it's a comedy, I don't know if it'd be best or worst to watch first if you do decide to watch anything together.
(My wife's personal favourite is "Some Like It Hot")