A Theatre District fixture is shutting its doors. The Drama Book Shop, a 100-year-old performing arts bookstore, is reportedly looking to relocate after facing a steep rent increase. The shop, known for its tremendous offering of play scripts, will shutter its store at 250 W. 40th St. in early 2019. The bookshop, which has been owned by Rozanne Seelen for several decades, is just the latest independent business to suffer from exorbitant rent hikes. "We knew it was getting too expensive,"…