I did this job yesterday, and based on the search and one post I found that claimed the driver side could be done without removing the brake booster (factory procedure), I plowed ahead.
The passenger side is too easy, so this focuses on how to do the driver's side bushing, buried deep under the brake booster and fusebox. Here's a thread with good pictures of the bushings: W126 The EPIC has BEGUN... Project "Sway" is Underway!

1. No need to remove wheels, or jack car up, as the drill is to raise the fusebox up enough to get your left hand in there to work. Disconnect and remove the battery.
2. Remove the three screws on the driver side securing the false firewall and
disconnect the vacuum line(s) going thru it, mainly the one with the check valve secured to it.
3. Cut or uncouple all the tie-wraps holding wiring and vacuum lines to the body and the fusebox (just those that will need slack to raise up the box)
4. Bend the false firewall forward to get it out of the way, so the harness going into the front of the fuebox has lots of slack.
5. Pull up on the fusebox and secure it with wire or whatever to the hood (see pic), as far up as it will go without putting undue strain on the wiring. I found it will go up just enough to get your hand in underneath, palm down.
6. With your right hand under the fender, and left under the fusebox, pull out the plastic cover. Shine a light in from under the fender to see what you are working on. Note the tabs and the 'hooks' on the back of the box.
7. You can put a socket and extension right on both nuts securing the steel bushing holder. The front is fairly easy to see, the back one requires a light.
Remove both nuts, then the steel retainer. Bounce the car a few times to help release it from the rubber bushing.
8. Use a floor jack and something long enough to push the sway bar up so
there is no pressure pinching the bottom of the bushing. See pic, I used a pipe clamp. Remove the bushing, noting that the split faces the rear, and the flatter side is down. Leave the sway bar in this jacked up position.
9. Insert the new bushing. I used some rubber-friendly silicone grease, which practically pulled the thing right into it's resting place around the bar. Remove the jack apparatus, watch through the fender opening that the bushing settles properly into the recess.
10. Replace the steel retainer, use locktight on the old nuts, or new ones, tighten down, and replace the plastic cover.
11. Put the fuesbox back down, wiggling to engage the 2 tabs at the back (which you now can't see because of the plastic cover), replace all wiring tiewraps and reconnect vacuum lines.
12. Return the false firewall to its position, getting the rubber grommets in place, put the 3 screws back, and you're ready for the other side.
13. The passenger side is a piece of cake. Just remove the battery, if not already done, the windshield washer canister, and the battery tray.
10. Remove the nuts, plastic cover, and steel retainer, replace the bushing (holding the sway bar up with a pry bar is too easy here), and put everything you took out back in.

Unfortunately, my old bushings were'nt all that bad (see pic with old one on the right), so I'm not really convinced this operation was much benefit in resolving my ride issues (see other thread one W126 ride). Hope this procedure is helpful to someone else though.

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1986 560SL
2002 Toyota Camry
1993 Lexus

Much thanks for posting this donbryce. No one has posted to this Thread since 2003 so I felt it is time. This is a time saving procedure for all of you out there wanting to change your front sway bar bushings but not the bar itself. I preformed the above procedure with relative ease and am VERY satisfied to have changed my drivers side sway bar bushing without removing the brake booster. Please note that you must be comfortable working in a VERY tight space. Exercise great patience during this job and you will have no trouble. Also, you must use GOOD judgment on how much pressure you can place on the wires entering the fuse box. Pull to tight and you got big trouble on your hands. You can see in the pictures below that I had very little room to operate the socket wrench once I got it on each of the bolts. The bolts come off slow but it is very much worth it. I started this project last night at 5:30pm. By 7:50pm I had BOTH sway bar bushings replaced, all my tools put away and I was standing in front of my sink washing up. See attached pictures for an idea of how much space you will be working with.

Cheers!

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Cousin Dave
83' 300SD 250k+ and going strong!

Take the best that exists, make it better!
If it doesn't exist, create it!
Accept nothing nearly right or good enough!

Kind words appreciated. Regarding that back/rearmost nut, I was able to go straight down onto it with an extension, about 8" long, right behind the fusebox. Same with the front one, which was almost completely exposed with the box up in the air. The extension allows you to spin the rachet, greatly speeding up removal. Again, nice to get feedback, especially on this very busy forum, where a thread can end up on page 2 in little less than a day!

__________________
1986 560SL
2002 Toyota Camry
1993 Lexus