Hello Jenny ... The bungalow bathrooms had the floor joists set 2" lower than the rest of the house, and had two inches of concrete poured in, and then the ceramic tiles set. We had our bathroom completely gutted, and originally, the contractor was going to remove the floor. The floor was deemed to be in solid structural shape, so they decided it was better to leave it and tile over it.
In your case, since your doing a gut and spending the time and money, it would only make sense to replace the floor. Also, it would be a good time to add a heat option to the floor. A simple, but dependable way is to use a heat mat under the tile. This is what we did, and it makes a huge difference in comfort. We also had the tub removed and a walk it shower installed.
A contractor I would recommend would be Brighton Home Products on South Pulaski in Chicago. Our contractor, Steve Draths, came out and examined everything and made recommendations. He has a really good crew that does quality work, no short cuts. Their tile work is exemplary as well.