Boat, which is a non-profit registered charity, said it put forward proposals to limit the use of the pitch from May to September when the theatre staged shows.
However, Mytum said nothing Boat discussed with the college had been adopted in the proposal.
BHASVIC principal William Baldwin said: “We always knew that our proposal would not be universally supported.
“As part of our submission, we actively engaged with local residents, stakeholders and user groups over a three-month period this summer.
“Planning is a democratic process and we respect the right of all voices to be heard.
“My hope is that the clear educational benefits, the promotion of physical exercise and the needs of young people and the community will lead to the approval of this project.”