bisexuality (n.)

1824, "having the organs of both sexes in one being, hermaphroditic;" see bi- "two" + sexual. The meaning "attracted to both sexes" is from 1914; the noun in this sense is attested from 1922, and compare bisexuality. Not in general use until 1950s. Ambisexual was proposed in this sense early 20c.

I suggest that the term ambisexuality be used in psychology instead of the expression "bisexual predisposition." This would connote that we understand by this predisposition, not the presence of male and female material in the organism (Fliess), nor of male and female sex hunger in the mind, but the child's psychical capacity for bestowing his erotism, originally objectless, on either the male or the female sex, or on both. [S. Ferenczi, "Sex in Psycho-Analysis," transl. Ernest Jones, Boston, 1916]

Bisexous (1838) and bisexuous (1856) also have been used in the sense of "hermaphrodite."

word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).

Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]