The good news is that the tub doesn't have to come out afterall. There does not appear to be any mold behind our under it. Yay!
The bad news is that the floor is very rotten and moldy. We knew that this was quite possible, but were still surprised at the extent of the damage. The whole bathroom subfloor will have to come up and we will be replacing the floor now as well. Our bedroom floor will still have to wait. Chris has taken out a chunk of the carpet that was a bit moldy and the rest seems to be ok for now.