Is there a prayer room at Bali airport?

Yes. Ngurah Rai International Airport (DPS) has mushollas in both the domestic and international terminals, before and after security, plus Masjid Al Ikhlas and Masjid Nurul Huda within the airport grounds. Several more mosques are a few minutes' drive away in Tuban and Kuta, which is useful on a long layover — see our mosques near Ngurah Rai Airport page for the full list and directions.