"The same result could be achived with a simple charge pump tho"
That's what it is, the advantage in using a mosfet driver would be the higher +/- output drive current.
"3.3v PWM to 12V PWM, then use a double diode and a capacitor."
You could use the PWM/EN signal, but you'd have to keep the duty within ~10% - ~ 90%.
I did think of mangling the PWM/EN and DIR/IN signals to keep the Vbs charged, or using 4 signals, a separate IN and EN for each half of the bridge, but I think producing an independent Vb would be better because it keeps the simple DIR/IN and PWM/EN arrangement you already have, and allows the full PWM 0% to 100%, but it's up to you which method you want to try!