My old girl had her nose bitten when away with her working. It's a bit scary as they bleed so much. I tied a scarf round her as dcs were present even though I was a 100% certain she wouldn't snap, I'd be fool to risk it with an injured dog. I bathed with salt water.
When I called the vet he said that's what he would have done / advised and to monitor it for 48 hours, and no swimming or letting her stick her nose in interesting things.
I was astonished at how quickly it healed as it was quite a deep tear.