Guns last. A revolver has changed very little in its design from the 1840s to today, and if the rigors of the post-civil war expansion west are a testament to anything, its that there's not much a lever-action won't survive. Coincidentally, many such guns take the powerful .45-70 Govt round, which I've been told, lends itself to being re-chambered.
A gun like that will last just as long as any bow, and be way more effective.
Also, as an archer, I can tell you a bow is no super-dependable, always ready and vigilant wonder weapon. It needs to be constantly unstrung (leaving a bow strung for more than a week will permanently twist the limbs), stored and kept out of moisture (prolonged exposure will soak into the wood, either expanding and weakening it, or foul the layers of glue holding the lamination together, quick immersion will soak and stretch the string, and foul the arrow fletchings, kiss your aim goodbye!), needs constant, almost everyday practice, and drawing and holding your aim is a huge pain. No waltzing about with your bow drawn like in movies, each shot is a calculated, thought-out effort. Also, using a bow powerful enough to actually kill will (no matter how strong you are) tire out your arms, making you less effective in melee combat.
Guns have none of those penalties, save for direct application of high moisture volume to the powder.
Also, making serviceable bows and arrows require a career's worth of skill. You're better off looting one than making your own.