transmitting bluetooth signal through cable

You are not going to get bluetooth traveling very far in water.
Bluetooth is a bidirectional protocol where a device switches rapidly between transmit and receive, therefore an amplifier to boost the signal is not going to be able to match this rapid switching.

what if I pick up bluetooth signal on the camera and convert it on site (on the towed underwater construction) to plain video signal and then send it through video cable?

Then you will stand a better chance of it working. Why not just have a camera that gives you video out in the first place?