the issue here is not one of running out of fuel, but to much fuel. when you are just slowly cruzin down the trail, the bowel gets completely full of fuel because the engine is hardly using any fuel. when you start going up a steep hill, the fuel will slosh out of the vents at the top of the bowel and dump raw fuel directly in to the carb, flooding you out.
the kit steelheadz is referring to does not keep the float open, but rather closed, so any hard bumps wont allow the float to bounce off its seat and allow a large in-rush of fuel into the bowel, which would over fill it and, again, spill out the vents and flood the engine. the kit should have also come with vent extensions to make it harder for gas to spill into the carb.
one trick you can use to help out is before you start a climb is at the bottom of the hill rev your engine. this will use up the gas in the bowell and as long as your using the lowest gear possable, to keep the rpm's up, you should have no issues. getting an off road kit for the carb is also a good idea.