Wordorigins.org

Bedlam is a Middle English form of Bethlehem, referring to the Judean city traditionally reckoned as the birthplace of Jesus Christ.

The sense meaning madness, uproar, or confusion comes from the Hospital of Saint Mary of Bethlehem in London. The hospital was founded as a priory in 1247 and is first mentioned as a hospital in 1330. By 1402 it was known for housing lunatics.

In 1547 the hospital was formally incorporated as a royal foundation for the care of the insane. The modern sense of a madhouse or place of confusion and uproar comes from association with hospital and dates to the early 16th century.

(Source: Oxford English Dictionary, 2nd Edition)