To be honest I didn't want to risk the noise attracting more zombies. I don't think it's a very good idea firing a gun when you don't need to.
That sounds pretty heartless, but I don't think suicide is ever the right way to go. Maybe if it was me infected, I'd think differently, but I didn't want to hand the gun to her. Plus, she's unstable. What if she turned the gun on me and demanded I cure her somehow, or she'd shoot me?