Your setter method looks correct, but you're getting an Access Violation because your FStarOff member is nil at the moment.
The usual is to create it at construction time and free it at destruction time.
constructor TMyComponent.Create(AOwner: TComponent);
begin
inherited;
FStarOff := TBitmap.Create;
end;
destructor TMyComponent.Destroy;
begin
FStarOff.Free;
inherited;
end;