Backfire seems like a good candidate. Not the XB-70, since it was never intended to drop bombs (ICBMs and SLBMs having taken over that role by the time the go-ahead for the two aircraft was given). It was purely a research aircraft, and had no weapons bay, nor could one be fitted without severely compromising combat radius.
B-1B nowhere near as fast as the Backfire (Mach 1.25 at altitude, vs. Mach 2.3), so even if we count smart bombs as iron bombs (and for the purposes of this question, we don't. By iron bombs, I mean dumb iron bombs) it wouldn't be the fastest bomber.
Must check bomber versions of the MiG-25, but I think that since it was originally designed as a fighter/ recce aircraft, it wouldn't count, in the same way that F-4s and F-15E (both based on air superiority designs, and F-15E still theoretically capable of an air superiority role with AIM-9s and cannon once you've got rid of all the air-to-ground stuff) don't count.
Did the Vigilante ever drop a bomb in anger? Don't think so, but might be worth checking.
Also remember that the USA and Soviet Union Russia are not the only countries, post-war, to have designed, developed and produced ground attack/ bomber aircraft.
Cheers,
Chris.
Cute and cuddly, boys, cute and cuddly!