Bat Out of Hell is a rock musical written by Jim Steinman based on the album of the same name. Steinman wrote all of the songs, most of which are songs from the Bat Out of Hell trilogy of albums by Meat Loaf including Bat Out of Hell, II: Back into Hell and III: The Monster is Loose. The musical is a loose retelling of Peter Pan and Wendy, set in post-apocalyptic Manhattan (now named "Obsidian"), and follows Strat, the forever young leader of The Lost who has fallen in love with Raven, daughter of Falco, the tyrannical ruler of Obsidian.

Who's music is the bat out of hell based on? OK. Let's think. My stream of consciousness:
To answer the question, consider the following: Steinman wrote all of the songs, most of which are songs from the Bat Out of Hell trilogy of albums by Meat Loaf including Bat Out of Hell, II: Back into Hell and III: The Monster is Loose. The answer is Meat Loaf.