There are many design issues with bike paths, but silence is definitely an asset. I think any deliberate noise-making isn't welcome.
A mirror is a useful tool to watch traffic behind you. If you don't want to have one, turn around often enough to watch traffic, and look out before you move left or right, jus as you do (or should do) before you change lanes when driving a car.
And when you pass, leave enough room to pass safely.
P.S. If everyone travelling on a bike path were to ring, why would one want to ride there ? The road would be quieter!