Bideon is the shipping of Gideon Gleeful and Bill Cipher. This ship has a very small presence in the Gravity Falls fandom.
The two are the main antagonists of Gravity Falls, and have been accomplices on more than one occasion. They are both megalomaniacs, and their shared interest is their hatred for the Pines family and desire to eradicate them, so the notion of the two pursuing a higher relationship (healthy or not, with a high possibility of betrayal) isn't particularly outlandish. The ship can also be depicted platonically, presenting Bill and Gideon simply as villainous partners in crime.
Bill canonically captured Gideon in Weirdmageddon Part 3: Take Back the Falls, trapping him in a cage and forcing him to dance cutely nonstop.