A bang-bang FET driver is not what you really want. To
get good stability and response the laser diode needs
to be kept lasing (just above lasing threshold) in the "zero"
state, and pulsed to the "1" state at even higher current.
Some sort of wired-or circuit, open drain current mode
is the ticket. If the FET driver has split high side and low
side legs then this could be just resistors, if that is not
too much of a speed impact.
With the bang-bang driver a limiting resistor to set the
max current is a good idea.