That's the bowl drain leaking. The screw beside the nipple is the drain screw, and is used to drain the fuel from the carburetor's float bowl, through the nipple and the attached tube (now missing) to someplace it cannot do any harm. Over time, sludge tends to collect on the bottom of the float bowl, and draining the bowl is a way to flush the sludge out. The screw acts as a drain valve. Dirt and sludge may prevent the drain valve screw from closing completely, or the screw may be damaged, thereby causing a small fuel leak through the drain.
You can try the following:
- Close the fuel stopcock, or pinch off the fuel line. Connect a short length of suitable tubing to the drain nozzle, just so you can catch any fuel that flows out or at least don't have it dribble all over the engine.
- Turn the screw counterclockwise a few turns. The fuel in the bowl will drain out.
- When the bowl is drained empty, remove the screw completely, and inspect the tip of the screw for damage. If the tip is worn or damaged, the screw should be replaced.
- Clean the screw and its hole. For the latter, a few q-tips might come in handy.
- Put the screw back in, and tighten gently. It should be tight, but not gorilla-tight :)
- Reopen the fuel stopcock or un-pinch the fuel line as appropriate.
- Observe the drain tube, check if fuel is still leaking out.
Chances are the problem will be solved, if not, it may be a good idea to remove the carb from the bike and disassemble the bowl for inspection and cleaning.