Again, to be clear, Bridge does not have any editing function, it simply opens the image in Photoshop. Photoshop invokes ACR and looks for a sidecar file when asked to open a RAW file. The difference you're seeing is due to Elements having a stripped down version of ACR (only the Basic, Detail and Calibration sections with none of the radial graduated filters or spot healing). The sections they share are exactly the same, except Calibration has its sliders removed. If Elements is sufficient for you "Photoshopping" you can overcome this by using Lightroom as your front end, which gives you full ACR, and then use Elements to do whatever layering and other edits you need. For a lot of photographers the functionality of those two products would cover 95% of what they would do with LR and PS.
Lol!