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This is Dr. Christian. Welcome to JustAnswer. You might need to either pull off the broken nail if possible or cut it back so that it doesn't get caught on things. The bleeding can be stopped with corn starch or flour. You can lightly wrap it to keep it protected with a light bandage and clean in once or twice daily with warm water. If the bandage gets wet or dirty then change it immediately. After a few days it should toughen up and improve. The nail should take awhile to grow back. If the toe gets inflamed, swollen or reddened the have it checked by a vet. He might need oral antibiotics at that point. If you have more questions please reply back.
Any bandage material from your pharmacy will work. Some bandage tape over that can keep it in place.