If it's dribbling like that it's probably a little grain of sand or something keeping the float valve from seating completely; it could be the float sticking like killa said although it could just need a slight adjustment to the float...
I'm not that sharp on injection but I can give ya a crash course on carbs, at least stock Banshee carbs. Fuel gravity feeds from the tank to the carbs, there's a little plastic strainer on the inside of the tank on the petcock that is supposed to screen trash from the bottom of the tank, although sometimes they fall off and/or get torn or whatever and things get through. If the system was dry and you turned the petcock "on" at the tank, fuel would flow through the lines straight to the carb bowls, through a type of needle valve that's connected to a float; the float and valve is just like a swamp cooler where as the float rises it pushes a valve shut. The needle valve itself is a little brass thing with a pointy rubber tip that seats against a machined brass seat; if a grain of sand or whatever lodges between the needle tip and seat it will keep flowing a small amount of fuel, which in turn will dribble out like at idle when the carbs aren't drinking alot of fuel. Same happens when the float sticks open, except it flows like crazy and just dumps fuel straight out the overflow; this can happen when you have the carbs apart or otherwise have empty bowls if the float decides to stay down. Sometimes just tapping the bowls with the end of a screwdriver will pop them free and float again, shutting the float valve, and you're good to go. Other times you hafta pull the carb and clean whatever is sticking the float at the hinge or whatever (the hinge is a little solid drive pin that is easily tapped out). Lastly you may just need to adjust the float height, which just happens sometimes, other times it will never need adjustment (there's other oddities that aren't common but do happen, like a pinhole in the float allowing fuel to enter and make it sink, or the pin falling out, or the tangs the pin goes into breaking off, etc. etc.). To adjust the height you pull the carb, take off the bowl, turn it upside down and measure between the bowl gasket surface and the bottom of the float (which is now the top of the float since it's now upside down); should be 20-22mm if I remember right. To adjust it just lightly bend the silver metal float lever between the float and the hinge.
Hope that helps. Oh and don't forget to put the choke tube back in place between the carbs if you pull them, and like killa said don't get the bowls reversed they are different one side to the other for the choke. Good luck.