I am a landlord and have faced this problem before. None of the experts addressed what I think is your biggest problem.... that is, what are you going to find when you open that floor up? I have had jobs where the joists below the tub were rotted away and the whole thing was opened up down to the crawl space! The clean up was immense, the job was just bigger than we planned on. So, I always look at any bathroom damage as potentially a BIG job.
(I have also purchased a triplex that I thought had some water damage under a nearly brand new bathroom; floors sagged - just a little - when you walked on them. I opened the floor, only to find that there had been a substantial fire in the bathroom [hence the 'remodel'] --- They had 'repaired' the joist with four 2x4s nailed all over the joist, they replaced wooden sub-floor with layers of cheap particle board --- then put beautiful tile over the top! Well at least I caught it quick-before the particle board swelled and crumbled.]
So, if it is just a little (new) water damage in just one small area. Your costs for a new floor, and repair (with labor) might be less than $600 in most of the country. However, if there is more damage and you need a contractor who must engineer something structural -- the price could go into $1,000's.
On the other hand you have no choice you must do it once you find this kind of damage. You can reduce the cost by handling the demolition and clean up and haul away. You can keep costs down with your choice in materials. Do shop around -- you would be shocked at what is out there cheap.
So - happy trails to you