The council has begun a consultation into plans to end free travel, except for pupils on low incomes or with special educational needs.
The authority said it was due to "budget pressures".
Mr Fitzpatrick said it would affect around 500 pupils at St Mary's.
At the moment all pupils who live more than two miles walking distance from their school are eligible for free travel.
The council said currently 1,900 pupils qualify at a cost of more than £730,000.
Vanessa Harvey-Samuel, learning and skills manager at Hull City Council, said: "If any changes are made, low income families will still be protected in line with statutory duties.
"However, we currently provide free school transport to pupils beyond our statutory duty. Given budget pressures, the city council has to examine all expenditure very rigorously."
The council is considering removing all dedicated bus services to some schools, but the consultation also has an option to keep those services "with the full cost being recovered through fares charged to those pupils not eligible for travel assistance."
Angela Martinson, head teacher of Newland School for Girls, told BBC Radio Humberside the future of the school could be in doubt if the dedicated bus services end.
She said: "In choosing our school and education for their girls, (parents) know their children can arrive safely at this school on dedicated school buses, and that's what they want.
"If these proposals go ahead I think the existence of Newland comes into question, and that worries me."
The consultation ends on 8 March
