Interesting question. Basic bicycle riding becomes feel rather quickly. But if you race , as I did, and want to go as fast as possible, there is a lot of technique that is not intuitive. To race at higher levels where technique becomes important, you must learn the skills from a mechanical standpoint first in a similar manner as Erik has pointed out in the 5 "S"s of Great Practice Thread. Road racing can involve a lot of tight turning and riding in a bunched up pack at high speeds. Mountain bike racing has a different set of skills to help you negotiate obstacles and terrain at top speeds. My bike club actually had training sessions for new riders to help them learn the skills. I learned first then later became a trainer.
It all becomes feel at some point. In some respects, I think the golf swing is harder to get the feel down that in bike racing. When I was in the groove racing, I never thought about the technique and only focused on one thing, "Where do I want to go". You are attached to the bike at five points and literally become one with the bike (stupid monkey?). I haven't got there yet with golf. I have had success with the short game, but with the long game I have not reached that level yet where I only think of, "Where do I want the ball to go?"
I'm not sure it's so much feel, as instinct..... especially in a group. You just react......pot hole = bunny hop.....no time to think about it, it just happens.