Hey Suntan,
On my girlfriend's D3 I followed these instructions on Droid Life:
How to: Manually Update DROID3 to Build 5.6.890 - Droid Life: A Droid Community Blog
I followed most of the posts and there were people saying that by updating this way you were able to keep root. That is false. There is the illusion that you did not lose root because you still have your superuser icon and /xbin/su etc... However, you are not able to gain write access or give superuser privileges to apps.
At first, when i ran the update through recovery, I did not remove any bloat nor unroot. The brief reading I did on the version they had on Droidlife (v. 5.5.959) said that it was not necessary. So when extracting the update i would get errors that said
assert failed: apply_patch_check ("/system/app/BooksPhone.apk. I understood that it meant there was a problem when it tried to update the Google Books app. I had frozen this app with Root Explorer. After this, i went back and unfroze all the bloatware then ran the update.zip off my SD card in recovery and it worked with no problems. When you boot your phone after applying the update it is common for it to take 3-5 minutes.
Now I am at the stage where the update is working fine but I want to re-acquire root. Creep said he re-rooted his using the one click. I'm going to try to unroot using the pete's tools and then attempt to re-root. If this doesn't work then I will have hit a dead end.
Update: I unrooted via Pete's tools v1.06 then rooted again and it worked like a charm. If you are having problems I have instructions for using the ADB method to add the SU script and Superuser Apk manually.