The biggest difference for me is that Bridge and Photoshop work off folders. You organise your images how you like them on disk, Bridge will let you rate them, add tags and so forth.
Lightroom, on the other hand, works off a database. You must import your files from folders into a Catalogue, into a hierarchy that can be completely independent of how the files were originally on disk. Folders can be simple, like a date 2012-02-15, but when imported into Lightroom can be put into a collection called "Sam's 30th Birthday".
Yes, Lightroom is non-destructive, but Bridge and Camera Raw are non-destructive too.
If your images are already well organised into folders on disk then Bridge and ACR allow you to work non-destructively. Lightroom is a much nicer and self-contained interface with some more advanced features than Bridge.
Apart from features and workflow, I feel this leap from organising on disk to organising in a database catalogue is an important consideration. You can always mirror the disk structure within the Lightroom organisation, but it's still a proprietary product that is organising your images - what if you want to switch to something else down the road? I guess it's just a matter of exporting it all out again. Maybe it's just me, but as slick as Lightroom is, I don't like handing over control of my images to a proprietary database.