How long does it generally take to transition to a WTP?

The WTB as noted by SFC (Join to see) is a unit designed for intense long term occupational and physical therapy fo SMs who have injuries that otherwise would prevent them from transitioning out of the military. These are usually the men and women who come back from deployments in very bad shape that will require potentially a year or longer to get to a level of rehabilitation that will be suitable for everyday life.

People don't usually transfer to the WTB for a MEB. The MEB process is pretty quick. WTB is usually for more complicated cases and Soldiers undergoing intense treatment. But if your command feels you warrant transfer to a WTB, it's about as fast as it takes to get some signatures on a 4187.