Is there a way I can pay just for my Apple Music account only

You can't change the Apple Music component of your Apple One plan. It's all a single bundle, not individual subscriptions. You could, as suggested already, subscribe to Apple Music separately, but if you kept Apple One you'd still be paying for the music component in that as part of the bundle. If you didn't want to do that then you'd have to subscribe to the Apple One components separately and pay a bit more for them jointly that way.

You can?

Just subscribe to Apple Music alone and not to other services