No one has brought up the psychology of no-hands....as in Digital Gee's comment that "cycling is 50% physical, 90% mental". The upright, twitchy criterium bike I've ridden for 18 years is easy for me to ride no-hands because I'm familiar with it and confident on it. My laid back sport tourer, 73 head/72 seat, is even easier of course.

It just might take a day, when you're feeling good, to just sit up at moderate speed, pull your hands back and have a breakthrough (hopefully nothing more broken than that)--

A friend told me a no-hands training thing to do is to practice switching from the hoods to the drops by simultaneously taking both hand off the hoods and dropping them to the drops. And then going back up. For a moment your bike will be "no-hands" but not enough to cause trouble. Gradually increase the no-hands time until you're ready to sit up!

Ultimately, bikes like to go straight (older, longer wheelbase bikes especially) and there's a bunch of physical laws keeping you upright.....despite what very normal anxieties whisper in our ear. It'll come.

P.S. When you're tired and balance/motor control is sparking and short circuiting on you....not the best time to learn no hands. Likewise when you just get on and roll out of the driveway, you're mind/body isn't fully "bikey" yet.