Adobe Bridge - can I tell it to always use sidecar XMP files for RAW formats only?

DNG,  JPG, and TNG files (not PSD) are all container files. That is, they act like folders to "contain" the various metadata files. 

But I think you may be chasing a false premise here. A 20 MG DNG and a 25 kb file will have the same storage size as the 20,000025 file with the xmp data. Separating the two will not make a difference. 

The JPG with xmp support has always been a bit of a tricky issue for many people: if you make adjustments to a JPG image and send that to someone who doesn't have Adobe Camera Raw themselves, they will see the JPG image without any of your adjustments. So, if you adjust a JPG file, you must do a Save as… before sending it out or sharing it on Facebook or other social media. 

Also, as you observed, captions, copyrights, keywords, etc., are all stored in the metadata as well. 

Similarly, if you move a JPG, TIF, or DNG file of its folder without the XMP file, it will appear as it did before adjustments. 

So, always saving XMP files outside of the files themselves really doesn't save you anything and potentially increases your frustration. And, I suggest you get two large external hard drives if your file size concerns you. You might consider doing what I do:

Keep in mind that any hard drive can fail. "There are two kinds of hard drive users. Those who've had a hard drive crash and those who've not had a hard drive crash YET.

Over the years, I've had several hard drives crash, and yes, I've lost stuff. Here's what I now do:

I have a 4 TB drive that holds all of my images and many documents. I have a 2nd 4TB drive that I use to back up my first drive. I manually do this at least once a week or more often if I've done a lot of work.

I have a 3rd 4TB drive I use for Apple's Time Machine.

I also use a cloud service in case the house burns down. Am I paranoid? No, just a realist. In a worst-case scenario, I would not lose much, at worse, sometimes. 

[Note: the 4TB is entirely based on what I need. Your needs may demand more or less hard drive space. Whatever you think you need, double it. Oh, the backup drives do not need to be SSDs or anything fancy or fast, just reliable. Also, look for backup software that can update your data as opposed to replacing your data. If you're on a Mac, I strongly recommend ChronoSync. If you're on a PC, I'm sure someone can make recommendations.]

Good luck!