How does a microcontroller load and execute a bootloader?
A microcontroller, just like any other CPU, starts executing code from a fixed address.  That address is often known as the "reset vector".

The address will be in the datasheet for the microcontroller.

Even on a PC it works like that.  The "booting" off a hard drive is about number 10347 in its list of things to do when it starts - the first is to execute code from ROM, just like a microcontroller does from Flash.