One-way missions:
USA - Some of the B-47 missions, and quite a few of the Navy nuclear missions were such that if the planes survived to drop their weapons and exit they could not make it to where there might be tankers to get back to the USA (or their carrier) and in many cases would not be able to make it to a neutral or friendly country to land or bail out. For those crews the "plan" was to get as close to the borders of the USSR as possible, and away from known nuclear targets. Also, hopefully, areas that were relatively lightly inhabited/few military forces and had terrain that was survivable (ie: not the middle of the Gobi desert etc). Fly until zero fuel then either controlled crash landing or bail out & hope you can make it to the closest "friendly" border.
USSR - In 1961 their midair refueling was quite limited even in the best of circumstances. Depending on where they took off from and what their targets were their jet bombers might have a shot at exiting the USA/Canada, unlikely any would be able to refuel to get back to USSR. No knowledge of whether those crews would attempt to get south of the border to bail out preferring Mexico etc to the USA/Canada. The Tu-95's had, in general, enough range to make it to the USA and back to the USSR - again somewhat dependent on where they took off from and where their target was.
Remember that the range figures don't account for flight patterns that zig-zag to avoid known air defenses, flights at altitudes other than optimum to avoid radar detection, using speeds that are less than most efficient, etc. Especially for the Soviet bomber crews, between North American air defenses and the range/refuel issues very few would expect to have even a shot at getting back. As noted, the additional problem for the Soviet crews was that, in 1961, unlike the US fliers there weren't any potentially friendly countries in proximity to their targets, neutrals at best and they were all in the opposite direction of home. US fliers, on the other hand, had several options for countries on the periphery of the USSR that were allies to try and get to.
USA - Some of the B-47 missions, and quite a few of the Navy nuclear missions were such that if the planes survived to drop their weapons and exit they could not make it to where there might be tankers to get back to the USA (or their carrier) and in many cases would not be able to make it to a neutral or friendly country to land or bail out. For those crews the "plan" was to get as close to the borders of the USSR as possible, and away from known nuclear targets. Also, hopefully, areas that were relatively lightly inhabited/few military forces and had terrain that was survivable (ie: not the middle of the Gobi desert etc). Fly until zero fuel then either controlled crash landing or bail out & hope you can make it to the closest "friendly" border.
USSR - In 1961 their midair refueling was quite limited even in the best of circumstances. Depending on where they took off from and what their targets were their jet bombers might have a shot at exiting the USA/Canada, unlikely any would be able to refuel to get back to USSR. No knowledge of whether those crews would attempt to get south of the border to bail out preferring Mexico etc to the USA/Canada. The Tu-95's had, in general, enough range to make it to the USA and back to the USSR - again somewhat dependent on where they took off from and where their target was.
Remember that the range figures don't account for flight patterns that zig-zag to avoid known air defenses, flights at altitudes other than optimum to avoid radar detection, using speeds that are less than most efficient, etc. Especially for the Soviet bomber crews, between North American air defenses and the range/refuel issues very few would expect to have even a shot at getting back. As noted, the additional problem for the Soviet crews was that, in 1961, unlike the US fliers there weren't any potentially friendly countries in proximity to their targets, neutrals at best and they were all in the opposite direction of home. US fliers, on the other hand, had several options for countries on the periphery of the USSR that were allies to try and get to.