I belive the NATO code name for the B52 was "Buffalo" and is probably the original source for "BUFF," although the translation you gave was commonly known (and recited) when you asked any what "what's that big m***f**r?" ... .
Lots of people shortened it to "BUF" and left out the "fat" part. The 4-letter version was used mostly by the "politically correct" speakers who often also substituted "Fella" (fellow) for F**ker when "informing civilians."
Although basically a high altitude plane, most B52 "combat" missions (and training runs, of course) included long runs in "terrain avoidance" mode below 500 feet AGL and sometimes down to 50 feet which made it "below the radar" to within less than 100 miles (12 seconds?) of the target.
Ref: AGL = Above Ground Level
Later "radar invisible" planes like the B1, B2, B3 usually get pinged at around 200 - 300 miles (according to rumors) if the target has recent good detection systems, and "visual contact" quite a bit farther if the enemy has aircraft up. Even though it's still short notice, the enemy scramble can still get off the ground to get to them before the bomb gets to the ground from the altitudes where they generally launch/drop them. They'll still get the target, but there's a small but real additional risk tradeoff for the crew.
All of the above (it's claimed) can launch guided cruie missiles from 300 to 700 miles out (again according to published rumors) so variations in penetration modes/methods make them all nasty if they're on "the other side."
Fortunately there have been few recent needs for "strategic bombing" of the kinds that were far too frequent in earlier deployments.