Wet a washcloth with cold water.
It's not as cold as it could be, but it's more comfortable than ice on your skin and it should still help.
Make a quick ice pack. Put ice inside a resealable plastic bag, and hold it on top of your nose. Crushed ice is ideal, but cubed works, too.
Keep frozen sponges handy. If you tend to get nosebleeds often, this trick can save you a lot of time. Get a new kitchen sponge, add a bit of water to it, and put it into a resealable plastic bag. Put the bag in the freezer, and pull out a sponge whenever you have a nosebleed — it'll be easier than hassling with ice cubes while you're bleeding.