True story here. Back in the mid 90's I was returning to running after a multi-year layoff. Things went well until I started to get my speed back and the ankle sprains got out of hand. I found myself (yet again) trying to keep my conditioning up on an indoor bike while waiting for my ankle to heal. This was like the 5th or 6th time in about that many months. So I said "screw it - I might as well become a cyclist". I had not been on a bike since maybe age 15 (late 40's at the time). And I ended up at an LBS and bought a pretty darn nice Bianchi (that I am still riding after some non-trivial upgrades).
The LBS guy took me out for a short ride just to show me how to shift and stuff (I had never been on anything except no-shift, coaster brake bikes) and that was in the early 60's. That was fine and the next day I went out for a 20 mile ride (my cycling conditioning was actually not bad given all the ankle sprains).
I went up a moderate climb in the San Jose, Ca area and was flying back down, having a great time. I got to a bend that was a bit sharp for my speed, braked a bit, turned a bit right and started to drift LEFT. I couldn't believe it and had no idea WTF just happened other than had a car been coming I would have been dead.
So I went a bit more cautiously back to the car, did some research, and as many others have said it 'just happens naturally' (but maybe not after 30-some years off a bike).
dave