Yes. From ADFG:

"The Municipality of Anchorage is Alaska's largest city. Its human population numbers about 280,000 in 2008, about 40% of the state's population. Residents also include 250-350 American black bears and 55-65 brown (aka grizzly) bears."

Gee, less than 700,000 people and two U.S. senators. Maybe you should get the bears registered to vote.

So, as far as the OP's question, and assuming the concern is strictly black bears, one tarp is adequate. I'd cook under the tarp, if weather or whatever other circumstances suggested this.

Storing food away from sleeping area is a great idea.

In areas where brown bears occur, I understand that more elaborate precautions are appropriate.