Headset bearings open to closed type
You will very likely be able to buy a new, sealed bearing headset for your bike. Without more information I can't tell you any more than that. It's not a particularly difficult job for a bike shop, but it can be tricky if you don't have the right tools.

Also, as pointed out in the comments, "sealed bearings" are better at resisting water and muck, but they're not waterproof and definitely not water-jet-proof.