With the appropriate licence or legal right to hunt them, it's legal to harvest bears; there's nothing saying that the animal has to be awake to do so (see Alaska hunting regulations). I'm not aware of any hunting regulation anywhere, Alaska or otherwise, that says an animal has to be awake before you can kill it legally. There are regulations regarding disturbance to wildlife you don't intend on killing: for example, Alaska Statute Title 16 Fish and Game; Chapter 05 Fish and Game Code; Article 7 General Provisions
Section 16.05.920. Prohibited conduct generally (wildlife “take” or
(a) Unless permitted by AS 16.05 - AS 16.40 or by
regulation adopted under AS 16.05 - AS 16.40, a person may not take,
possess, transport, sell, offer to sell, purchase, or offer to
purchase fish, game, or marine aquatic plants, or any part of fish,
game, or aquatic plants, or a nest or egg of fish or game.
Section 16.05.940. Definitions
In AS 16.05 - AS 16.40 (33) "take" means taking, pursuing, hunting, fishing, trapping, or in any manner disturbing, capturing, or killing or attempting to take, pursue, hunt, fish, trap, or in any manner capture or kill fish or game;
Rules such as that are rather common, at least in North America, not just Alaska.
So while the combination of the two might seem odd, it really isn't. And it wouldn't be confined to Alaska. I work in environmental assessment in Canada and we routinely issue terms and conditions that you can't go near bird nesting areas to avoid disturbing them, yet people able to legally harvest bird eggs obviously can.