The Questioner: Does bleeding from the nose (ar-ruʿāf) break wuḍūʾ (ablution)?
Shaykh Muqbil: A nosebleed does not nullify wuḍūʾ; there exists no [authentic] evidence that it nullifies al-wuḍūʾ. There had come a weak ḥadīth (حديث ضعيف – ḥadīth ḍaʿīf) that is nullifies it; but it is is not authentically established from the Prophet ﷺ. And the Companions of the Messenger of Allah ﷺ used to pray while they were wounded. Thus, it does not nullify or invalidate [wuḍūʾ].
However, if he fears that he may soil the masjid (with the spilling of his blood), then he may leave and wash (his nose out), and then return and continue on with his prayer.
And Allah is the One whose help is sought.
Ijābat al-Sāʾil, p. 32.