Bring a large pot of water to a boil and add in asparagus. Cover and cook for 4 minutes. Use a slotted spoon to remove and transfer immediately to the ice water.
In a bowl combine mayonnaise, dill, capers, lemon juice, pepper and salt. Mix well.
Remove asparagus from the ice water and pat dry. Stir into the mayonnaise mixture. Cover and refrigerate for at least 1 hour.
When you are ready to make the bruschetta turn on the broiler. Once hot, place the baguette slices on a baking sheet and broil for 2 minutes or just until lightly toasted. Remove from oven and rub with garlic clove.
Spoon chilled asparagus mixture over the top. Serve.