my Honda shadow leaks gas from a hose under the bike?

Not all the time.

Replace the hose!

You talking the little plastic clear hose? it is probably the battery acid overflow hose... or it is the black plastic or cloth hose that is the gas overflow hose - perfectly normal as long as it isn't dumping out a lot of fluid... that is what it is there for...If you fill the tank on a hot day or while on the center stand, the gas will expand a little and overflow or when on the side stand it will overflow... Just don't fill it soo much! Or start riding right away to burn off the 1/4 inch of gas so it won't still overflow!Keep on biking!!

there are drain or overflow lines coming off the carb(s) and leading to the ground just behind the motor.If the bike has been sitting up over the winter your floats(in the carbs) could be stuck and when you start or try to start the bike it keeps pumping fuel in until the float gets to it's maximum height preventing any more flow until needed.These floats could be dirty and stuck telling the fuel to keep flowing.Do not run the engine.There could be gas in the crankcase.Smell inside the oil fill hole and see.Solution:clean carbs,change oil and filter.

I agree that it the float is a little sticky in your carb.A quick add of some Seafoam to your gas and a squirt into your intake should clear everything up.Good riding.

Does it leak constantly? Or does it leak only when the tank is full? I had one that would leak right after I filled the tank, especially on hot days. It could just be cold gasoline in the tank expanding as it warms up and is coming out the overflow.