The output is floating/connected to a symmetrical power supply (so the negative is not connected to ground but -V)
That makes the level shifting so much more a pain in the ass.
Output voltage is ±50V.
(most articles are about the fact that the output is connected to GND, which is easy)
I'm confused, what's your actual topology here? Negative input->negative output? Positive input->negative output? Symmetrical input->two-quadrant output?
Unless you're working on something with unusual voltage/current requirements where you have no other choice, I have a hard time imagining an engineering case for NOT using an integrated solution at least for the switch driver. Sure, you might save a bit of money, but at the expense of board size, much higher component count, and more difficult layout--especially when you consider the niceties that come free with an integrated bridge driver, like UVLO and cross-conduction protection.
That said, a basic level shifter for a high side switch might involve using a ground referenced current sink to turn on a PNP to pull the gate up to Vbootstrap, and another ground-referenced current sink driving a current mirror referenced to Vbootstrap that sources current into an NPN that pulls the gate down. If the supply voltages are particularly high you may want to incorporate a darlington stage so that you can reduce the amount of current required in the level shifter stage. The main trick (with any method) is to ensure that the slewing of the switching node doesn't interfere with the operation of the level shifter and potentially turn on the high side switch at the wrong time, leading to shoot-through and cooking the bridge. Another option could be to capacitively couple a differential pulse to set/reset a latch referenced to the high side switch--using a differential signal will reject the slewing of the switch node, again to prevent misbehavior. And finally, there's the transformer option, which would eliminate the need for a bootstrap voltage, but is probably not going to be any cheaper than using an IC.