Yes it does, as a bonus action is an action on your turn...
, per PHB page 189.
Also Crawford answered thisCrawford answered this question specifically in a pair of tweets, as well as clarifiesclarified Bonus Actions.:
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.