Hi @DannyN,
Stopping water from leaving the bathroom is about all you can do to prevent further damage.
Similar to @AlanM52, I am wondering why there is no lip or something to stop the water from leaving the bathroom.
Is it possible to get some photos showing the bathroom?
Is there a reason so much water is finding its way out of the room?
Is your shower not containing the water as it should?
We'd need to see the bathroom to offer further advice, but it seems like there could be an issue with drainage in the bathroom if water is able to find its way out of the bathroom in a large enough quantity to cause that damage. If that is the case, then the issue might require the drainage in the bathroom to be addressed and a water stop of some kind installed at the door.
When we can see some photos of the bathroom, I can assist further and recommend some solutions.
Jacob