Praise be to Allah.
The Standing Committee for Academic Research and Issuing Fatwas states:
“If the matter is as described then your fast is valid , because your getting a nosebleed was something involuntary so the fact that it happened does not mean that you broke your fast. This is indicated by a great deal of evidence from the Shari’ah, such as the verses in which Allah says (interpretation of the meaning):
“Allah burdens not a person beyond his scope.” [al-Baqarah 2:286]
“Allah does not want to place you in difficulty.” [al-Maidah 5:6]
And Allah is the Source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and Companions.” (Fatawa al-Lajnah al-Daimah li’l-Buhuth al-‘Ilmiyyah wa’l-Ifta, 10/264, 265)
It also says:
“If a person has a nosebleed involuntarily whilst fasting , his fast is still valid.” (Fatawa al-Lajnah al-Daimah li’l-Buhuth al-‘Ilmiyyah wa’l-Ifta, 10/268)
And Allah knows best.