Who do you work for usually the Bridging Document comes from the HSE Department.

You say 'rig', so presumably you are in the upstream oil & gas sector? It's far too late to prepare the bridging document AFTER you arrive in dock, as it should be part of the pre-planning - but if that's what you've been asked to do!!!! Basically it's a 'who does what' between the separate Safety Management Systems in place for the rig and the dockyard when they are working alone, e.g. for emergency response, work permits, potable water & food, use of lifting equipment, provision of PPE, etc. There's a guide available on doing this on the Step Change in Safety website - though it's aimed more at organisations working together in the field.