Up until the mid-60s, when the U.S. had a 17:1 strategic superiority over the Russians, it was assumed that the U.S. would take damage, but still survive as a country. The USSR and WARPAC countries would not. Until SIOP-60 in 1960, each service had its own war plans, and there was very little coordination: Navy planes off of carriers would hit a Soviet naval base, and a few hours later, in comes a B-47 or B-52 to service the target again, even though it's already slag. Ditto for missiles: Regulus cruise missiles from subs or surface ships would reach a target, and a bomber or carrier plane comes in sometime later to put more fire (literally) on target.
As far as SAC having fighter escorts, they did have dedicated fighter-escort wings up until the mid '50s, with the F-82 Twin Mustang in the late '40s-early '50s, then the F-84 up until 1956. The F-108 Rapier was designed not only as a high-speed, long range interceptor for Air Defense Command, but at LeMay's request, could also serve in the fighter-escort role, especially for the B-70. Lockheed's F-12 was also intended as a fighter-escort, since there was a planned B-71 version of the SR-71 on the drawing boards at Kelly Johnson's Skunk Works, but the AF elected not to pursue the B-71. The F-108 died in 1959, and the B-70 a year later, but the latter was resurrected as a R&D effort with two aircraft, one of which crashed, and the other is now at the USAF Museum in Ohio. The F-108 and F-12 would have had AAMs with nuclear or conventional warheads, and if the former are being used, would have been burning Soviet interceptors out of the sky, as Ivan had nothing that could've caught either fighter. They wouldn't have been escorts in the traditional sense, but fighter sweep would be more like it, as they would've gone ahead of the bombers to kill Soviet interceptors.