Yes, BULLPEN is a Scrabble word!

Letter values in Scrabble US: B 3, U 1, L 1, L 1, P 3, E 1, N 1.

Is it a valid word?

BULLPEN is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

a place on a baseball field where relief pitchers can warm up during a game
a large cell where prisoners (people awaiting trial or sentence or refugees or illegal immigrants) are confined together temporarily

Also: detention cell, detention centre.