After the battle at the Tower in which Sadeas abandoned Dalinar, the majority of Cobalt guards have been killed. As such, Dalinar has to supplement his forces. To do this he decides that he wants Sadeas' bridgemen and trades his Shardblade to Sadeas for them.
As the best trained and most trusted of the bridgmen, Bridge Four is made into the new King's Guard.
Captain, you and your men are in a unique position. You spend your daily lives around the king. You don't see the face that is presented to the world, you see the man. It has ever been so for close bodyguards.