Ms Avery said banning the tails completely would disappoint a lot of people, who had bought them and learned how to use them safely and properly.
"I have two girls myself who will be very disappointed they will not be able to use their tails in the pools. It would be a real shame for it to be gone completely."
She said a complete ban might encourage people to use them in open water which was extremely dangerous.
Ms Avery hoped to talk with Bay Venues about holding special mermaid tail swimming sessions, with close supervision and in an area of the pools which would not endanger other swimmers.
BaySwim manager Simon Leach said they had considered having sessions for people to swim with mermaid tails but would have to discuss it further before anything was decided.
He said banning the tails from the pools showed the public they were not safe to use without one-on-one supervision, which Bay Venues could not provide.
Mr Leach strongly discouraged anyone from using the tails in open water, saying currents, poor visibility and the lack of a side wall or lane rope to hold on to made it very risky.