Yes, you can play the movies you have bought/rented on your TV by installing BookMyShow Stream app on your TV from the TV app store (Currently available on AndroidTV, AppleTV, FireTV).
Alternatively you can also cast the purchased movies on your TV from your phone using Chromecast or Airplay.
Casting option is currently not available for downloaded movies.
NOTE: Kindly login with the same contact details entered while buying/renting a movie.