Are you referring to the entire bumper cover or just the lower air dam? The lower air dam bolts to the upper bumper cover the way I described. I thought that's what you were asking about. The top of the bumper cover, from factory, came with rivets across the top (under the front edge of the hood). Those rivets don't hold the bumper cover to the car. Instead, they hold the outer cover to the inner structure, as the bumper cover consists of a flexiblr plastic outer cover over an inner header piece. A lot of folks think those rivets need to be drill out to remove the cover, but that's not true. If you have plastic push pins, is it possible someone already removed the rivets? I believe the rivets are black, so they kind of look like push pins.
To remove the bumper cover from the car, you have to first remove the lower fender skirts (on each side). They are screwed into speed nuts iirc and tend to get rusted and hard to remove. You will need to pull the inner fender liners, or at least loosen them in the area where some of the screws are located. There are several screws along the bottom radiator core support (or down there somewhere), bolts between the front of each fender, and a bunch of bolts in the engine bay around where the headlights are.
The lower air dam also has a couple oddball "specific" pieces underneath. One is a flat plastic "splash guard" type thing held on by screws. The other is a hard plastic piece, but I can't remember what it looks like. Both of those pieces can be left off, if you don't care too much about originality. I left them off, but have them stored somewhere.
Once the entire front bumper assembly is removed (headlights still attached), you can flip it over and unbolt the lower air dam from the upper bumper assembly. If yours are like mine, the fasteners will be rusted. Half of them will break at the studs when you try to loosen them. I think what I did to fix them was to turn them upside down and hammer the rusty studs out of the rectangular washer pieces. Then, I put new bolts through them and jb-welded them in (to keep them from spinning, since you can't get a wrench on the backside Once installed). A tack weld would have worked too.
This is all just from my poor memory lol! I currently have a pace car and 79 cobra with the front bumpers removed, as well as another pace car and 82gt (same bumper/air dam) with the bumpers installed. If you need any pics or some help with it, let me know and I'll do what I can to help. These are a pain, but take plenty of pics, keep hardware organized, and take your time and it'll be fine. Sorry about the super long post, but I just remember all the grief I put myself through while dealing with it and thought I would share everything I could think of. Shoot me a pm if you need to. I don't even care to talk it over on the phone if you would like.