Dave, you are correct about bent = crazy, but it is just one of the slang meanings picked up by this word.

My son (a lawyer), says some lawyers refer to crooked clients as bent. This meaning, first appearing in print in 1914, has persisted. Originally used in the U. S. by criminals (Jackson and Hellyer, 1914, "Criminal Slang"), it has extended to England (examples from the OED), used in The Times, 1958: "I had known for years that certain members of the Brighton police Force were what we call bent." The first UK appearance was in the "Sunday Pictorial," 1948.

Of products- Brophy & Partridge, in their "Songs and Slang, 1914-1918, pub. 1930- "Bent, spoiled, ruined."

Of course the term has also been applied to homosexuals.

An old term for metal work, in which the materials are bent into shape, is "bent work" (not slang), 1858.

Also a carpentry term, a section of a framework of a framed building (1815).