I went from a Trek Navigator (an upright comfort bike) and a Giant Transend (an upright commuter), to a Fuji Cross Comp CX bike. It did feel wierd to me at first, I had never been in drops in before, and being spread out like that made me feel really unstable. I don't think I rode on my hoods for probably 3 months after getting it, and didn't go into the drops until maybe 6 months after having it ( I have brakes on my shifters and across the straight part of my drops ). Being in that position with skinnier tires is just totally different, but you get used to it. The only way is to ride!!
Recently I got really crazy - I swapped out my stock wheelset with the knobbie tires on it for Easton EA90 wheels with 700x23 slicks on them!! Ok, that only took about 10 minutes to get used to, mostly the extra speed I now have