Glad you asked. There are a bunch of candidates – from primates to parasites. However, after careful consideration, my favorite bisexual organism has to be [drum roll please] SHEEP!! Specifically rams!
LOVE THESE GUYS! I mean their on and off again romances with odd farmhands have fueled some of my best blog posts.
And when it comes to their own kind they still like to experiment, 10% of rams (males) are down with mating with ewes (females), as well as uber-into getting it on with other rams. No wonder they are the animal of choice for condoms.