The story
From bi- + -sexual, via the French bisexuel (bi-, sexuel). Attested since 1792 as a synonym in botany for "hermaphroditic" ("having male and female parts"). First used of sexuality in Richard von Krafft-Ebing's 1886 Psychopathia Sexualis (in German) and Charles Gilbert Chaddock's 1892 English translation thereof, due to the theory that people were naturally attracted to the opposite sex and so the brain or mind of a person attracted to "both" sexes (or to the same sex) must be partly of another sex and thus "hermaphroditic".
Etymology from Wiktionary, CC BY-SA 4.0.