Reference: Fataawa Ramadhaan – Volume 2, Page 475, Fatwa No.414
Fiqh al-‘Ibaadaat – Page 196
Question: What is the ruling regarding blood coming out of the mouth, nose or any other part of the body of the fasting person?
Response: This [flow of blood] does not affect him because it occurred without him intending so. And if he had a nose bleed and a lot of blood came out, then his fast is [still] correct and nothing is required of him.