Perhaps the easiest answer would be that a Faulkner story, or a Faulkner, without bourbon would be like a fraternity party without beer -- completely unrecognizable. While in one way, as a responsible professor, I'm tempted to point out that Faulkner might well have lived a happier and more productive life were he sober, and I would not want to encourage alcohol abuse, on the other hand, Faulkner's long, rich, convoluted sentences, and narrative style filled with tangents and asides, weaving from past to present, and from memory to reality, derive part of their richness from the way they draw upon the style of the extended yarn told in some old, run-down bar in the deep south, with the spiderwebs festooning every corner mirroring the Spanish moss draping the trees of the bayou outside.
Part of what causes the comedy in "The Bear" is that it is about a drunken hunting trip, in which people are doing wild and stupid things with the strange, quasi-rational motivations of those just drunk enough to have lost all inhibitions but not far enough gone to be incapable of carrying out their wild ideas.
Without the bourbon, Ike could have been a successful hunting guide for rich city people, building up a slick and professional business. He would have been wealthier and more successful, but perhaps less interesting.