I read the service manual and they say to remove the bumper in order to flush
the old coolant. Is that true? Is there another way to flush the old coolant without
removing the front bumper? I really need help on this before this afternoon! Thanks

 

There should be a red valve on the lower drivers side of the radiator. See if you can reach in there to turn it. Otherwise you will have to remove the bumper or at least put it in the service position.

 

What do you mean, put it in the service position Jest? By the way, Thanks

 

You have a B5 right? There are two big long bolts on the underside of the bumper. They come out. From there the bumper can be unhitched and pulled away from the car (front ways) about 6 inches.

Check out this link for some help (it's for an S4, but essentially the same) on removing the bumper. Stop at step 8, that is the service position.