How to bid a job repairing hidden damage in stages to avoid a "time and materials" job
My suggestion should make this a whole lot easier all around. Do the demolition on a DIY basis and clear away all the debris. The demolition phase work requires basic skills and simple tools that are not expensive. 

This will open up the structure of the whole room back to framing, subfloor and ceiling joists. I would say that then you would be ready to bring in a contractor to bid on repairs and upgrades to the room and structure. Nothing should be hidden at that point.

As you take on the DIY part of the project you are sure to have some questions about that process. This site can be a big help to get answers to the questions that arise.