How do you remove the front bumper from a 99 blazer?

 

Are you talking about the bumper cover (plastic) or the rebar (the metal part?
Here's how to get the cover off. Once you remove the retainers, the sides slide out of the side retainers
Click on the picture, then click on the circle, then the yellow dot to magnify

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i'm taking off the entire front bumper (bumper, strip, and valance). What is the easiest way to access those bolts?

 

Ok, start by removing the front grille.
Open the hood. Support the hood with a prop rod.
Remove the grille by gently pulling evenly in order to disengage the retainers.
Remove the grille from the vehicle
Then Remove the nut and the bolt that retain the brace to the bumper impact bar.
Remove the connectors to the front turn signal lamp. Refer to Park/Turn Signal Lamp Replacement in Lighting Systems.
Remove the fog lamp connectors, if equipped. Refer to Front Fog Lamp Replacement
Remove the nuts and the bolts that retain the bumper impact bar to the frame.
Remove the bumper impact bar from the vehicle.
Remove the side extensions from the bumper impact bar, if equipped

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