Preheat the oven to 450 degrees F (230 degrees C). Line a baking sheet with parchment paper.
Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels. Chop.
Make an aioli by combining mayonnaise, garlic, chives, salt, and pepper in a bowl. Set aside.
Roll the puff pastry out into a 12-inch square. Spread aioli onto the pastry quickly and top with bacon, tomatoes, and salmon. Roll up jelly roll-style and cut into 12 equal pieces. Lay on the prepared baking sheet and let chill for about 30 minutes.
Bake in the preheated oven until golden, about 18 minutes.