Typically the rules for jumping are that you have the engine of the donor vehicle off, you connect the positive lead to both batteries, then connect the grounds, making the last connection be the ground on the donor vehicle, preferably to a grounding point on the chassis rather than the battery post. (Making the last connection away from the battery reduces the small risk that the spark that tends to occur with the last connection could possibly ignite any hydrogen gassing from the battery.) Then start the donor vehicle to raise overall system voltage to the typical charging 14V-14.5V (compared to the 12.8V or so of a resting battery) which provides some extra voltage to accommodate the loss in the cables and connections. Then start the dead vehicle.
With the much larger capacity of a car battery providing plenty of current to turn over the comparatively small starter motor of the motorcycle, the need for starting the donor is lessened. That being said, there really is no significant risk of causing damage to either vehicle if you start the donor. Assuming there are no major electrical faults in either vehicle, the systems are completely compatible.
- Mark