The bumper cover goes on top of the aluminum bumper, an extruded frame with several channels and a solid top. One way to mount the lamp bases is to use molly bolts or expanding screw plugs, or to rivet them using long aluminum rivets that go through the top of the bumper itself. Tape might work, but may not stick for long on the plastic.

Remove the air dam beneath and use a flashlight to look up there and plan your work.