So really, Batman only used guns to kill living people on that single occasion (since vampires are undead), and even then he stated that it was an exception to his moral code. This meme out there that "Batman used to use guns," as if he were some sort of Punisher-type killer for a significant amount of time, is a gross distortion of the facts, an attempt to impose modern tastes for more violent "heroes" onto the character.
I don't think it's a case of imposing modern tastes by spotlighting his gun use, but rather hanging a lamp on the fact that Batman is a derivative of the pulp character, the Shadow. Whenever I read those early stories, I don't see a prototypical Punisher. Instead, I note all of the "homages" (a generous term) to Walter Gibson and his work on the Shadow. The images of him wielding guns are more evocative of what came before (the Shadow and other pulp vigilantes) than what came after (the Punisher and his ilk).