To enter Bedlam you must first complete a quest for the Mistress of Admissions who can be found just outside the dungeon.

To gain access to the Peerless boss, the Monstrous Interred Grizzle, you must complete a quest for the Librarian.

The Bedlam Crypt, which is a champion spawn, can be entered through one of the buildings in the cemetery.

Bedlam Crypt