How rapid is the drain? Do you have any devices or accessories that use voltage while the scooter is off (e.g. alarm system)?
First thing to do is check that all the connections are good. Pull the seat and take the nose off. The connections we're concerned with are the stator and the regulator. Check that each wire is secure in its connector and should be making firm electrical contact. While were at it, make sure the ground wire (green) has no resistance to the frame ground.
Once that's done, unplug the stator connector with the yellow and white wires. Leave the bullet connectors together. Start the engine.
The yellow and white leads get tested against ground. They produce AC. At idle, they don't necessarily produce that much voltage, maybe between 7 and 12, depending on where you set your idle. When you rev up to about 5000 rpm, each lead should produce in excess of 30v AC (not uncommon to see 45). If you have this, the stator should be fine. Plug it back in.
Now the yellow line should be limited to 14.5±1v AC. The white may or may not have the same limit. Move up to the nose where the regulator should be housed. Here the yellow and white leads should give you the same readings as they did back at the stator connector. The red lead will give you between battery voltage (which should be about +12.5v) at idle and +14.5±1v DC at rev.
Now for the less kosher tests. Pull the fuse. Now you should get only the stator voltage on the red lead, DC limited to the 14.5. Shut the engine off and put the fuse back in. The red should test battery voltage. The yellow and white leads should test absolutely zero volts, AC or DC.
If any of the tests in the previous two paragraphs fails, it's the regulator/rectifier that's bad.
For references, the following generic manual may be of help:
www.scootdawg.com/downloads/GY6_50CC_MANUALscooter.pdf