Inverter Mosfet Driving with Isolated Totempole Supply
To drive the low side FET gates, the gate supply needs to be commoned with the low side of the bridge. To drive the high side FET gates you need another supply that is commoned with the source pin for each leg. Most gate drivers do this using a bootstrap configuration where a capacitor is charged up using the pumping action of the FETs switching - so if you have the bridge in one state for any length of time obviously the bootstrap cap starts to discharge, so there are arrangements with a separate bootstrap oscillator that do that.
 It's usually easier to use a gate driver chip than to use a discrete solution. This is a FAN7382 but most are similarly configured.

One final point - running this at 1MHz is going to be challenging, if not impossible. Charging and discharging the gate capacitance to get a FET to switch at that frequency requires careful design.