Mix oregano, garlic powder, and basil in a small bowl. Pour olive oil into a separate bowl. Brush bagel slices with olive oil on both sides; wipe any excess oil from pieces using a paper towel. Sprinkle a small amount of oregano mixture onto each bagel piece. Arrange seasoned bagel slices onto a cooking rack.
Bake in the preheated oven until bagel chips are browned and crisp, about 1 hour. Let cool 10 minutes.