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There are a number of possibilities of what might cause this.
A dental infection can abscess into the nose and drain bloody fluids.
A weed seed or other debris in the nose can cause infection and injury.
A bacterial or fungal infection is another possibility.
If the dog got into rodent poison sometimes the first sign of the bleeding that goes with that is a bloody nose.
A tumor can also cause this.
You can read more about nose bleeds in dogs here including first aid info
and more about nasal issues in dogs here
and that site has a good picture of how the inside of a dog's nose looks.
Hope this helps you!