Bishop Makarios of Minya said the wounded had been taken to a hospital in Beni Mazar, around 200 kilometres (120 miles) south of Cairo. ISIS claimed responsibility for that attack.
Egypt says fighting Islamist militants is a priority to restore security after the years of turmoil that followed the Arab Spring protests in 2011. He had earlier said the bus was approaching the monastery.
Egypt's President Abdel Fattah el-Sisi mourned the victims of the attack on the Christian bus, vows to push ahead with campaign against militants, on Twitter. He expressed his deepest sorrow and assured his "determination to continue our efforts to combat terrorism and to pursue the perpetrators".
Friday's attack is the second to target pilgrims heading to the St. Samuel the Confessor monastery in as many years, indicating that security measures in place since then are either inadequate or have become lax.
Church spokesman Bouls Halim said the death toll in Friday's attack was likely to rise.
The attack took place nearly at the exact location where 28 Christians were killed by Islamist militants in 2017.
In Minya, the scene of Friday's attack, Christians constitute the highest percentage of the population - about 35 percent - of any Egyptian province.
Egypt is carrying out a significant security and military offensive, mainly in Sinai, also on the border with Libya, to defeat militants behind a series of attacks on security forces and civilians, including Christians.
Egypt's Copts have in the past accused the authorities of making only token gestures to protect them from such attacks.
In 2016, at least 25 people were killed in a suicide attack on a Christian church.
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