Bridge not saving changes to files in Camera Raw

Let me guess: Are you working on JPGs?

Here's what's taking place: In ACR, you never change a single pixel; you are only changing how the image is "perceived." If you open that image in ACR, you can see the changes, but you must open an image in ACR to see those changes. If you want your computer and anyone else who does not have ACR to see those changes, you need to SAVE those changes into a new JPG, TIF, (whatever format you want). This "burns in" those changes so anyone can see the results.

This is different than a raw image, where most applications cannot even view a raw file directly, and it has to be opened in ACR first.

Think of ACR as providing filters that you look through to see the image after your adjustments. The catch is that you can only see the results when you're looking at the image IN ACR. (Within Bridge, you're always looking through those filters). 

To have those changes as part of the image, you need to "burn" them into the image. This happens if you save the image into another JPG, TIF, PSD, etc. There are several ways to do this: you can open the image in PS and, from there, save the image. BTW, if you try to open a file that you've adjusted in ACR directly into PS, it will open up in ACR first so that the filters can be set before opening in PS.

From within ACR, you can click on this icon in the top right corner of the ACR window.

And from there, you'll get a window that gives you a number of save options.

One more thing: if you ever get started working with raw images, you'll find out that you cannot change a pixel in a raw image; it can only be adjusted with these. And again, you cannot change a pixel in a raw image, only how it looks after you've run your adjustment filters in ACR. 

So, why is all this good? Let's say you took a great photo, used today's PS to make a bunch of adjustments, and then saved the document. Now, your original image is GONE. Now, let's say that next year's PS has some spectacular new features that, if you had it this year, could have done a much better job of fixing your image. But that image doesn't exist anymore. You saved it with last year's ability which isn't as good as next year's ability. This whole thing is what's behind "non-destructive editing." It's a good thing.