The Warlock invocation One with Shadows grants invisibility until you "move or take an action or reaction." Does taking a bonus action end this invisibility?
Yes it does, as a bonus action is an action on your turn, per PHB page 189.
Yes, taking a bonus action breaks the invisibility of a warlock's One with Shadows. […] A bonus action is an additional action on your turn (PH, 189). Apart from its special rules, a bonus action is an action.