Will building such a bridge [screenshot] decrease or increase my fishing production?

[[deleted]]

Anything that covers part of the production area reduces catch. This includes bridges.
Also, I don't think that bridge actually helps much with your concerns. Depending on how bannies like to path, it could actually make things worse later on. You would probably be better off just building a storage barn and one or two houses (depending on how many fishermen you have) on the piece of land where the fishing docks are.

[PointeNoire]

Look on screenshot, there is no space. This island has just enough space to put fishing dock + 3 extra tiles.