Does anyone here know if it is possible to change a headlight bulb, without removing the bumper?
Also where can I find the clips that hold all of that together?

 

You can get to them through the fenderwell but in my opinion, it's a whole lot easier to unscrew the bumper where it meets the fender (1 on each side, Philips), pop out the 4 clips at the top of the bumper grill (you see them when the hood is up) and then just pull the bumper forward, unbolt the headlights, and do an easy swap. No need to undo any clips at the bottom of the bumper. Might be more steps but I will do this every single time instead of trying to compete with my wheels for access.
What clips are you referring to that "hold all of that together"?

 

I only had to remove the 2 or 3 clips through the wheel fenders towards the top and front. Then, you can slide your hand in. I've replaced both bulbs with oversized LED bulbs this way including the rubber grommets for the bulbs. I don't particularly recommend going LED, but if you do, you'll have to readjust the headlight direction.