Yes, you can organize your images in folders just as you can in Bridge.
Having said that there is one fundamental difference between Bridge and LR that you need to keep in mind to do your image organazation satisfactorily.
Bridge is a browser based program. That means that Bridge "sees" whatever is on the hard drive. If you change image file names, folder names and/or move images or folders in your OS (Mac Finder / Win Explorer), Bridge will have no trouble "seeing" the images under their new name in their new location.
That is different in LR. LR functions as a data base (called the catalog). It does not just "see" what is on the hard drive(s) - that's why images have to be imported. LR needs the catalog to represent the state of your hard drive(s) correctly. Only LR can read and write into/ from the catalog; no other program can do that. When you re-organize your images via your OS (changing names of files / folders or moving images / folders) this change is not written into the LR catalog. Then you have a discrepancy between the actual state on your hard drive(s) and the LR catalog resulting in "missing image" messages and a situation where the folder structure that LR displays is different than the one on the hard drive..
Whenever image organization is done outside of LR, these changes are not only NOT reflected in LR but also LR is now unable to find images or folders.
Then you get greyed-out images, question marks on the frame of thumbnails (in Grid View), question marks besides your folders, and your new folder structure will not be displayed in LR.
This is one of the most important things to keep in mind: Unless you are very proficient in LR, always, always do all the image management (changing folders, moving, renaming image files) in LR. If you do this, LR will automatically keep track of all changes. If you don't you'll come to grief.
Does LR show you any images greyed-out? If this is the case with some (but not all) images within one folder, click the small question mark on the frame of the thumbnail (in Grid View) and navigate to the correct location of the image. If the file name has changed you'll be asked to verify that this is the correct image.
If you see any folders in the folders panel with question marks besides them, do the following: Right-click the top-most folder in the hierarchy that shows question marks and navigate to the correct location of this folder. LR should then find all sub-folders within the parent folder provided that the structure and names of folders has not changed.