Goodness! The busiest bear day I've ever had in SNP was, I think, three. They don't worry me much in the backcountry unless there are cubs; it's the ones that show up at the campgrounds, the ones used to people, that worry me. When I take my son camping there in Shenandoah, I'll bring pepper spray, something I've never done before outside grizzly country.
If you haven't already done so, you should submit this in the climbers' log; it's quite a story!