Re: What makes for a bike that you can ride no hands
Headset bearings is one thing--they should be straight (faces parallel), in good condition, greased and not overtightened.
Fork rake & trail should be right. A lot of fork modifications mess this up, some are even sold this way. Using a 20" front wheel on a 26" frame + fork causes this too.
Handlebars center of gravity should be "neutral", meaning they don't stick out far forward or far behind the head tube axis. Think of the classic ten-speed road bike handlebars, or straight MTB handlebars.
A big (26") front wheel helps compared to a smaller (20") wheel, as does a fat/heavy front tire.
If you use a seat-back (or a sissy bar) you may not be able to ride no-handed either.