This feeling of letting it "wash over you" is a verbal construction that is very helpful and apt for some, but others may describe it's different. Some people may start to think of it as "experiencing these feelings with more remove" or something. It's something that takes practice often done with guidance from a therapist or psychologist.

For many (this is not universally true), what is experienced as "anxiety" is like a preset program or routine that auto-executes across cognitive, behavioral, and emotional channels. CBT isn't a cure, but helps you interrupt the program during its cycle or before it starts by inserting new and different programs that don't auto-run without effort. As you sense your anxiety spiking ("awareness training" may be needed to get this early insight), you engage in behaviors or techniques to prevent the normal cycle of anxiety spiraling and calm the nervous system.

It is effective, but it is not a magic trick and takes practice.