You can choose to bring the grappled creature with you, but it takes 10 feet of movement.
Bait and Switch says:
When you’re within 5 feet of a creature on your turn, you can expend one superiority die and switch places with that creature, provided you spend at least 5 feet of movement
When you use Bait and Switch, you are using your available movement, so the rules for using it apply, that is, bringing a creature with you costs twice as much movement.
On a 5 foot grid, since you cannot move only 2.5 feet, you must move 5 feet, which costs 10 feet of movement when bringing a grappled creature along.