I really would not want to ride up 330 unless the road is closed (which they used to do for ride around the bear, not sure if that's still a thing anymore). The road up the back way via Onyx is a much nicer place to spend an afternoon on the bike and you can grab chow / fresh water in Angelus Oaks both ways. Park at the ranger station at the base of the hill (mill creek visitor station). If you start early enough, you'll have time to drop into Bear Village for some chow before you climb back out.
Watch out for weather, it just snowed up there yesterday.