I need to use IR2302 or IR2104 gate driver for my synchro buck application, but I could not find a good explanation about the capacitor between pins VB and VS, I guess it is called bootstrap capacitor but I could not understand what is the purpose and what should be the value or even a type for this capacitor. Is a regular film capacitor will work or I need an electrolytic capacitor or Should the capacitor be a polarized or not? I couldnt find any information about this in the datasheets of both.

 

A nice low ESR capacitor will be fine, like a ceramic capacitor.

The whole concept is to store some charge in the capacitor to create a voltage higher than Vcc to drive the top side MOSFET gate.
This is a clever solution - with one very important caveat - you cannot drive the bridge HIGH and leave it there, the gate charge will leak away and the high side MOSFET will start to turn off.

The bridge must me switched low to recharge the bootstrap capacitor, that's how it works.
Most bridge circuits are used with PWM so it's constantly switching - no problem, just don't try to drive it high with a DC signal.