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The main bike ground normally comes off the negative battery terminal and grounds the chassis at the starter. There are secondary grounds like the one you describe at the rectifier to stop ground loops that form because the steel frame is not that good a conductor. Without the secondary grounds, the starter ground might be at zero volts but the rectifier ground might be at +1 volts or -0.5 volts, etc.
Hooking to a car is not a problem unless you start the car. The scooter and car regulating systems do not work the same. For example, if the car system puts out +13.5 volts and the scooter normally does +13.0 volts, the regulator system on the scooter will try to absorb the extra voltage by attempting to load down the car. The problem is the car system can put out so much more power that the rectifier system on the scooter can fry before it can absorb the extra power.
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