Which lights are 9003? My regular headlights were H4, and my aux lights were 1156 - this is a 94 Si. Did the later years have different bulbs?
I changed out all four front lights a few months back, and did NOT have to remove the bumber.
To the best of my memory: to change out the headlights, unplug the harness from the bulb. Turn the bulb until it's "unlocked" from the housing, then the retaining spring/arm should push it back into the engine bay area, where you can remove the plastic insulating material between harness and bulb, and then change the bulb itself. At least, that's how I remember doing it.
For aux lights, I remember it being much simpler, almost like plug 'n' play. I'm not sure about 9003's, though.