There are lots of myths about Jim Bowie, and lots of biographies which propel them. It was very probably his brother Rezin who invented The Knife, for instance (see pp. 581-82, and 745 in the book by Davis, cited below). Whether it was or not almost doesn't matter, though, since it was Jim Bowie's life and death around whom the mythology developed, and he is a fascinating figure of his time.
By March 6, during the second week of the Alamo siege, he had been sick with typhoid fever for weeks. He was probably so weak that he couldn't even get out of bed, where he was killed with a shot to the head.