System Preferences->Security and Privacy
You need to grant access. Bridge will ask and if you decline then you can't open those folders.
Be sure to get ALL of the preferences
Go to your System Preferences and select Security and Privacy (found in the top section). Now click on the Privacy setting (last tab). Now click on the lock on the bottom left and provide your Administrator code. Now select the Full Disk Access option and click on the "+" symbol. This will bring up the standard Mac Open window and let you add any application you want or need to have full access. Look for Bridge, select it, it will now appear in that window and make sure it's checked. Next, go to the Files and Folders option and do the same thing as above (although there's nothing to check, just add. Close everything down and see if that makes it all work.
Please let me know
[Note: these images are from an older OS, the process is the same.]
Also, if things are still not working reset your preferences
Quit Bridge (if running). Just before clicking on Bridge in the Dock or double-clicking the application for the Mac, press Command-Option-Shift. For PCs, press Control-Alt-Shift. Then open Bridge BUT KEEP your fingers on those keys until you see a window pop up. From the window, choose “Reset Preferences," "Entire Thumbnail Cache,” and/or "Reset Standard Workspaces.” In your case, choose "Reset Preferences."
The fact that they are greyed out is OK. When there's nothing to add, Apple doesn't bother to give you access. If there is, then Apple lets you check or uncheck the options.
Your third screenshot showing the locked Desktop did show something VERY important: that is not the Desktop folder; that's an alias of the Desktop folder. I do not have time to verify on my end right now; I've got to leave, but navigate TO the Desktop, not an alias of the Desktop and see if that works. My guess is that it will.
Let me know!