I'm too much of a noob to play DS1. I have run out of bullets right at a save when a couple of buggers attack me. I give upback onto games that don't scare the shit out of me.
Tip if your running out of ammo, only carry one or two guns, then you will only pick up ammo for those guns. Only upgrade those guns, you save ammo in the long run since you dont need to make as many shots since your doing more damage.