There are waterproof bluetooth headphones. I have a cheap pair somewhere. But, Bluetooth doesn't work underwater (range is just a few inches). I do water jogging with my Watch and AirPods but I keep my arm movements on the surface so that my Watch isn't submerged. (I want the Watch to track my workout.) You can see a discussion of options at https://h2oaudio.com/blogs/news/bluetooth-and-water
I swim once or twice a week, using these headphones and the Apple Watch.
The music is on mp3 the BT doesn't work under water , probably not the greatest sound and difficult touch sensor on the headphones, but once your master the sensors and clicks you're ready to swim like an hour or so.