I installed a 32" TV in the bedroom behind the sliding closet doors. Similar setup on the Bullet. IIR, there is about 3.5 inches of depth for a TV and a mount. I bought
this type of mount of Amazon., which has a very low profile at only 0.6 inches. Then I purchased a TV that had a maximum depth of 2.8" inches or less. Best Buy's Insignia series fit the requirements and I have about 0.5 inches to spare for the closet doors. I added a nylon buckle strap along the bottom of the edge of the recessed area to secure the TV tightly. It worked out well.