I don't think I've seen a bushed headset yet.

Many of the cartridge type headsets have a compression ring (centering cone?) that is often split as it doesn't have bearings riding on it.

Anyway, I'd start looking at cartridge bearing upgrades if yours is actually bushed. It would likely make the headset smoother turning and safer.

Do you have some photos of the steer tube?

What size and type of steer tube/fork/stem does the bike use? Threaded? Threadless? Some kind of threadless with a locking compression spacer?