Sexuality is determined by four things: the person's chromosomes, internal sex organs, external sex organs, and psyche. Bisexuality covers all of the area here seeing as sexuality is on a continuum and not simply classified as a binary stagnant thing. Some may argue hermaphrodites, pseudo-hermaphrodites, and other IS people don't fit into one gender group. However, they consist of male and female sexual organs and also combinations of X and Y chromosomes. Regarding people that are transgendered, they are biologically of one sex regardless of how they manipulate their body through procedures or hormones.
Furthermore, it should be noted the difference between omnisexuality and pansexuality. Omnisexuality's definition includes people that are bisexual and have pedophilia, necrophilia, zoophilia, etc. Further clarification of these words can be found in the easy to read "Sexologies" journal from the European Federation of Sexology.