Eggplant Jeff

What danno said, with the caveat that perhaps you're carrying too much weight on your arms? How's the fit generally on your bike? On a MTB you should have a fairly upright posture and your arms shouldn't bear all that much weight.

However, no matter what riding posture you have, you'll usually have to lean back and carry most of your weight on your butt when you are riding one-handed. When I do it usually I sit up straight on the seat and have one hand only lightly on the handlebars.

I can ride one-handed in a normal position, but not for extended periods (long enough to signal a turn or whatever). In that case you have to have very tight control of the handlebars... as Danno said, your weight on only one side will tend to push the handlebar away on that side (turning you) so you have to pull back by about the same amount... Takes some practice.

One way to think of it is it's half way to riding no-handed. If you were riding no-handed, your butt has to carry all the weight and your torso's going to be more or less straight up... you could bend over the handlebars but it would be very hard to maintain that posture. Riding one handed is in a lot of ways halfway between normal and no-handed.

[edit] thought of a suggestion.

Practice riding two-handed, but with almost no weight on your hands. Lean back as far as you can torward a straight-up posture, and just controlling the handlebars with your fingers (both hands). Rather than gripping the handlebars, you just have your fingers on 'em lightly. That way you can get used to the posture you'll be using. And once you've got riding with your hands very lightly on the bars, taking one hand off is easy... because the other hand doesn't push the bar very hard.

It'll be easier to do if you're riding at a reasonable speed, not super-slow... because you don't need as much force to control the handlebars at speed (they tend to stay straighter on their own). Maybe 10 mph or so.