Why is the bathtub water backing up into the shower?
The rate of flow and effective pressure from the bath is more than the drains ability to drain. This is normally associated with a clogged drain but if you say it's clean. The drain problem is somewhere after the pipes run from the shower. I had that problem previously and it ended up being roots in the drain. 
If the shower flows right after you let the water out then there is a blockage close by, but I would guess that the shower only gets water after a few minutes.