The Bering Circle does not exist however if you mean the Bering Sea it is located to the southwest and west of mainland Alaska. It is does not for part of the Arctic Ocean but is an arm of the Pacific Ocean. The Bering Strait connects the Arctic and Pacific Oceans and lies just south of the Arctic Circle at the northern edge of the Bering Sea.
North to the Arctic & to the South is the Pacific.
The Bering Sea is in the Arctic. It is between the Alaska (to the East) and Russia's Kamchatka Peninsula (to the West).
The seas that surround Alaska are the Gulf of Alaska and the Pacific Ocean (South), the Bering Sea, Bering Strait, and Chukchi Sea (West), and the Beaufort Sea and the Arctic Ocean (North).
The Bering Sea is fairly shallow, but yes, submarines transit the Bering Sea regularly heading to and from the Arctic.
The Bering Straight
There are several important land forms and waterways in Alaska. Mt. McKinley, the Bering Strait, the Bering Sea, and that Arctic Circle are just a few.
The Bering Strait separates the two lands and links the two ocean.
The Bering Strait links the southern part of the Arctic Ocean (called the Chukchi Sea) to the Bering Sea.
The Bering Strait is actually an ocean gateway between the Pacific and Arctic, so 'gateway to the Arctic' as a description of Bering may be more exact.
The Bering Strait is the narrow (about 53 mile wide) channel of water between Russia and the U.S. state of Alaska. The strait is at about 66 degrees north latitude, a little below the Arctic Circle, where the Bering Sea (within the Pacific Ocean) meets the Chuckchi Sea (within the Arctic Ocean). The International Dateline passes between Russia and the U.S. through the center of the Bering Strait. Please see the Related Link for a map illustrating the location of the Bering Strait.
Arctic Ocean (to the north) Bering Strait (to the west) Bering Sea (to the west, but south of the Bering Strait) Pacific Ocean (To the south)