Please make sure you have up to date version of Camera raw(9.1.1) for Photoshop first.Download the latest here Camera Raw plug-in installer
Once you install latest Camera raw,Close Bridge and Photoshop
From Photoshop>>File >>Browse in Bridge, open a Raw file in Bridge
Check if you have the Camera raw icon back or you can right click the Picture and open in Camera raw,
Also let us know what is the issue you are facing with Lightroom?
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ACR needs to be given an xmp file together with the photo file that has been edited in LR. Normally LR does not make xmps unless you click Cmd+S or from the menu bar Metadata/Save metadata to file.
The info from elie-d is correct. Lightroom is a complete standalone application and by default saves the work done in its Catalog file, so while you are working with Lightroom its reads and writes to/from the Catalog file.
Bridge / Camera Raw on the other hand will read and write to .xmp sidecar files so you need to use the option in Lightroom to also write the info to .xmp.
Also there is some things that Lightroom does not write to .xmp which a specific to Lightroom like, collections, virtual copies, history etc.
see more info at the link below.