My wife and I use GMRS radios for when we get too far apart. I have some that can use headsets, but we don't use the headsets. As I said, we just use them for when we are on a trail, like the GAP, and are out of sight of each other. We don't always have cell phone reception there. GMRS requires a license, but no test, you simply pay for the license, and it covers your family, so your license is good for your wife as well.

There are other bluetooth cycling communicators out there. Google turned up some. A friend of mine used to use some with his wife, but I don't recall the brand.

Here is one that seems to still be available. It mounts in a helmet. https://www.terranosystems.com