Well, that's not good.
So I ran to the bathroom, removed my shirt, and started trying to blot at my nose with tissues. It became apparent this wasn't working, so -- after calling Gretchen upstairs to try to get the blood out of the shirt -- I followed the classic treatment and went to lie down until the bleeding stopped.
Happily, this worked.
I had been going to take Katie and Julie to gym night at the school this evening, but Gretchen went instead, as a recurrence of the nosebleed there would have been more than a bit entertaining. :)