Do I need resistors before and after bootstraping a MOSFET?
The diagram you have shown on its own is not bootstrapping. It is just a low-side gate driver.
But for what you drew, you do not strictly need the MOSFET gate resistors. It has its uses to control the rise/fall times, ringing, and noise (which may prevent some circuits from working properly), but since no static current though it's not strictly needed.
You do need the base resistors for the BJTs if the PNP is on top and a NPN is on the bottom because there is static current and will short like a diode. If you have a NPN on top and a PNP on the bottom, then a base resistor is not needed because each transistors will prevent a base-emitter short in the other transistor.