An Arizona man apparently planned to commit suicide by bear. He told the local detective that "he had wanted to go up on a mountain, shoot up a gram of heroin and 'be bear food.'" I'm not sure that really qualifies as suicide by bear. I think that is more "suicide by heroin overdose," with the hope in mind that bears will then eat your corpse.
A truer attempt at suicide by bear was made in 1911 when a woman in Lima, Ohio had to be rescued after maliciously inserting herself into a cage full of bears.