Sorry, your statement "I can continue to use Bridge 5.0.2.4 perfectly well... " seemed like things were working well. So I wasn't entirely sure what your issue was.
Adobe products have to be in harmony to work in harmony. When Bridge-CS6 was written, the engineers had no idea what would be in today's ACR or Photoshop. Sadly then, they could not pre-write code to take advantage of it.
Also, if you do not have a license to use a current Photoshop Family suite, Bridge cannot take advantage of the newer ACR. So yes, Bridge may work just fine, but it will be without the functionalities of ACR.
You can certainly continue to work with Bridge-CS6, and if that's all you need and you're getting what you need out of it, GREAT! However, if you want more, I'm sad to say you'll have to update your applications.
https://www.adobe.com/creativecloud/photography/compare-plans.html