http://sheldonbrown.com/gloss_an-z.html#angle
Angles
In general, bicycles with shallower, "slack", "relaxed" angles (lower numbers) tend to be more stable and comfortable. Bicycles with steeper, more upright angles (higher numbers) tend to be manuverable, but less comfortable on rough surfaces. Shallower frames tend to have longer wheel bases than more upright frames; bicycles with shallower head angles normally have more fork rake. All of these factors contribute to the riding characteristics cited.
Your problems with riding with one hand or none may be directly related to the geometry of the bike, not your riding skill.
My wife learned to really ride when she was about 60 - although she had ridden a bit before, she never rode much as a kid.
However, there are some things that come naturally to someone who has ridden since childhood which still seem a bit foreign to her, particularly when it comes to any kind of risk taking. But, nine years later, she still rides a mean bike!