Is it bad when your pet rat gets a bloody nose?

That isn't blood, the red discharge around your rats nose is called porpythrin.

It depends how much there is; porpythrin is normal for rats to have every once in a while; rats also get it around their eyes, too. Don't worry about it unless it appears that your rat's "crying blood" or sneezing red liquid or they have so much on their nose that it's drpping.