How does one construct a bazooka using 75 ohm coax for the radiating
portion and 50 ohm coax for the feed (as usual)?

Phillip, The best thing would be to short the shield and inner conductor of
the coax and use it as your typical wire dipole. The old standard 468/f(mhz)
should work as a starting point. Do an swr sweep, or trim for lowest swr at
your transmitter.
A 1:1 balun at the antenna is good engineering practice to minimize
transmission line radiation. Be aware that the magical 1:1 swr may not be
possible feeding a dipole with 50 ohm coax.
Modern literature on the subject of bazookas indicate they will give broader
bandwidth at the expense of decreased efficiency. Depends on what you want
from your antenna.
73 Gary N4AST