You cannot hide that you are a convert. Whatever their reasons may be, I've known many converts/conversion candidates who adamantly felt that it was no one's business if they are converts and that no one has the right to ask them if they are a convert.
That's all well and good, but they're still going to find out, so every convert needs to get used to admitting to being a convert and create some canned responses to common questions. Almost no one will ever ask, "Are you a convert?" It's much sneakier than that, not to mention almost always completely innocent conversation.
We've discussed Jewish Geography before, and those conversations will be your downfall if you don't want to talk about your conversion. They always start innocently enough, trying to locate people you know in common. But then it gets more personal:
"Where'd you grow up?" ... "Oh, there aren't many Jews there! What's the community like?"
Umm...I wasn't involved in the community.
"So you weren't religious growing up?"
Nope, sure wasn't. I started going to synagogue in college.
"Well, what were your parents raised?"
This is the question that'll get you every. single. time. I'm luckier than most. My parents were atheists and I had no religious upbringing, so I sound like any other Jewish kid raised by secular parents. Most converts aren't this lucky. After all, the last answer you want to give is "Southern Baptist." Once you do, the gig is up and you are exposed as the convert you are.
Every once in a while, when I say my parents are atheist, the determined person will ask "Well then, what were your grandparents?" This is relatively unusual, but sure to expose just about every convert in America.
Other questions that lead towards self-exposure include:
Where is your family from? Translation: "Which little shtetle in Europe does your family come from? Maybe we're related!" Yay for Ashkenazi assumptions!
Where was your family during the war? Translation: "How much of your family died in the Holocaust? Let's share war stories!" More Ashkenazi assumptions.
Why did you start going to synagogue/getting Jewishly involved? This one is a toss-up. It could go nowhere or expose you for what you really are. Dun dun DUN!
In summary, Jews like to talk about being Jewish. And that means they're going to ask you questions about your Judaism, and there's an approximately 75% chance that they're going to back you against a wall and make you admit that you're a convert. Get used to it and start coming up with canned responses that you feel comfortable giving to a complete stranger.
Once the cat is out of the bag, 95% of those conversations will then turn to how awesome you are for converting and detailed stories of every single person they know who has converted. Approximately 3% will result in a confused face and the question, "Why would you do this when you could remain a gentile and not be bound to all these laws?" And the other 2% will be rude, condescending, or abruptly end the conversation. Your mileage may vary.