You misunderstood. Perhaps an unfortunate use of words on my part. I did not say we have had bombers loaded with nukes circling Russia 24/7. We have continued to fly long range strategic bomber missions since the end of the Cold War, many of them with Russia as the focus.

On Sept. 27, 1991, President George H. Bush ordered the termination of Strategic Air Command's alert which began in October 1957 following the Soviet launching of the Sputnik satellite. The alert forces ceased operations the next day, beginning the successful conclusion of the Cold War. SAC alerts had been 24-hour, with precise requirements for ever-faster takeoffs dependent on the type of scenario in test.

http://www.af.mil/news/story.asp?storyID=123008783

Bomber command was transfered to the Air Combat Command of the US Strategic Command the same day. Since then we have flown "Global Power Missions" to demonstrate to the world our capabilities. Out of inertia or lack of another major target out there, Russia has been the focus of many of these Global Power Missions. I would imagine they have found that unnerving to say the least.

http://www.globalsecurity.org/military/ops/global-power.htm

The B-2's ability to reach deep into enemy defense networks and disable command and control, infrastructure, integrated air defense, and other high value targets makes this aircraft a valuable force enabler. The B-1, the backbone of our conventional bomber fleet, will employ its high speed, maneuverability, and improved defensive systems to attack the next level of medium and low threat targets with large payloads of highly accurate point and area munitions. In so doing, it will strike the bulk of the targets attacked by bombers. The B-52's contribution early in a conflict will be limited to a standoff role, but will follow up with direct attacks on lower threat targets when enemy defenses are weakened. This combination of aircraft meets the mission requirements of geographic commanders while providing our nation the maximum return on its investment in land based airpower.

http://www.fas.org/man/congress/1997/h970611acc.htm

Since B-52's will act in a standoff role as a platform for cruise missiles, they would not actually have to enter Russian airspace to strike. Any approach of B-52's towards Russian airspace COULD be a prelude to war.
I'm sure we would not be happy if Russian bombers made habit of coming up to the edge of our airspace. Oh, that's right, I guess that's what's going to be happening from now on.

P.S. The Tu-95MS is also a cruise missile platform
(I'ld love to ride in the the tail-gun position in the Tu-95. The droning of the engines is hypnotic, like riding home fron the Drive-in in the back of the stationwagon as a kid. And it's cold with altitude. All bundled up, with that droning vibration running through the plane, they'ld have to wake me up if we ran into any action.)