Does my Delaware State Parks annual pass cover my admission fee to Bombay Hook?

Nope. Bombay is a national wildlife refuge. Entry is $4/vehicle/day.

Or you can pay $12 for the annual pass

Must have a National Park pass. You can pick one up there.

I would think not, Bombay Hook is a National Refuge, not state.

No it's a Federal Facility.

National and state parks are separate

No it doesn't. Bombay Hook is separate from Delaware State Parks. It's a wildlife refuge. $4.00 per vehicle.

You can buy a annual pass for national parks. State and national parks require different passes.

You can also buy an annual pass good for all of the refuges.