You can't use a bonus action to make your mount Dash. What you can do, though, is make your mount Dash without using any actions at all.
The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.
So as long as your mount isn't intelligent, you can tell it to Dash anytime you want without any actions. You can shoot your bow, have the horse move 60 feet, then tell your horse to Dash and move another 60 feet, dismount and move 15 feet yourself (assuming you have a move of 30 feet) and still have your bonus action available for your personal use.
