Green’s Dictionary of Slang

batcave v.

[see prev., i.e. Batman’s HQ as a place of rest from crime-fighting]

(US campus) to sleep.

[US]Eble Campus Sl. Fall 1: bat cave – sleep: He’s been bat caving all afternoon.
[US]Eble Sl. and Sociability 31: As in the general vocabulary of English, slang permits the compounding of words of various grammatical classes, with the exact relationship between the parts unspecified. noun + noun is the dominant pattern: the verb batcave ‘sleep’.