Headset stiff when the bike hasn't been ridden for a while

It sounds like it needs a service, which is pretty easy to do. There is likely to be some dirt built up in inside, perhaps as a result of some water ingress, or because the grease is old and gumming up.

It's likely that the movement warms the grease up, and lets it move freely. it will need a service sooner or later. This is something you can easily do yourself, and it's likely to benefit from a cleaning, and a smear of new grease.