The $200 is pretty universal for smoking - so they likely just used that as the base for your water damage. You may be looking at a bill for much more than $200, but I wouldn't expect the bill to be lower than that.
If higher, be sure and get a detailed report stating the costs and damages.
The room likely won't be rented (if you checked out) due to needing to let the carpet dry (depending on the amount of water). The room below (if one) may not be rented either and have damage.
If still there, take pictures of the tub. While there likely won't be a drain in the floor for overflow, there likely should be some type of drain/mechanism to try and help overflowing water, but even then, that's of limited use. I don't think any tub/sink drainage system can clear water faster than what the faucet is putting in.