How much power is dissipated as heat in a 12V MR16 Led Bulb
LEDs are better driven by current sources than by voltage sources. This means that LED bulbs tend to have a small current regulator embedded in them.

This current regulator can be something sophisticated like a buck regulator to something as simple as a capacitive dropper.

These regulators will provide the current even when you drop the voltage (up until they cannot create the voltage needed to light up the LEDs). And because they are active (in the case of switch-mode power supplies) or reactive (like the capacitive dropper) they won't create excess heat like a simple resistor in series would.