Interesting thread. I have a few things to add, from the speed running perspective (QdQ guys).
They started experimenting with bunnies already during -98, see for example
this E1M1 demo from may -98 by Ilkka Kurkela (Mineral from clan CMF). It sure wasn't the full blown bunnying we got later, but it was jumps stringed together from a first strafe jump. If someone feel interested enough it will be pretty easy to work out a bunny timeline from the full demo database over on SDA.
My feeling is that bunnying it kind of trickled down from the speed run world to the QW online community by guys like Mineral (and, I guess, by my humble self :-)). If you remember the DM3 games between 9 and DR in august -98 there was quite a stir (CHEATING SWEDES!) when Xenon jumped the red armour gap using strafe jump, simply because almost none in the online quake community knew about those things. But of course Xenon did, being a speed runner
himself.
I also say Sectopod for the guy professionalizing the bunnying, but whether he did it in DM or when playing CTF with us in Ace of Spades I can't recall - might have to go digging for old demos