The problem is NOT with the type of battery, or with the type of vehicle it it happens to be currently connected to
That's right. You could jump your bike with a nuclear power station if it had a 12V DC outlet
But back to the initial question: What might have been damaged?
First let's look at how a diode works (first pic). It will forward current if its cathode (the end the triangle is pointing to) sees a smaller potential than the anode. On the other hand, if the voltage at the anode end drops below the voltage at the cathode end, it will block current.
The second pic is showing the alternator/rectifier circuit. Actually there are three alternator windings and six diodes but for simplicity, I'm just showing a third of it.
If hooked up correctly, current will flow from the alternator winding through the diode to the battery if its voltage is above the battery voltage. If the alternator voltage is below ground potential, the diode on the ground side will become conductive. Since the alternator winding is delivering AC, its voltage will change from, let's say +15V to -15V to +15V and so on.
If the polarity of the battery is reversed, the ground potential will see +12V. Both diodes will see a positive potential at their anode ends and 0V at their cathode ends. So they will both become conductive and short out. Consequently a lot of current will flow through the diodes and the wires that connect them to the battery. The diodes can handle huge amounts of current but eventually they will pass out. The wire with the largest resistance will start glowing before the diodes go up in smoke.
So if you are lucky and the battery was connected for just a very short time, the rectifier should be ok, but you will have to check the wire harness and connectors.