Actually, it was built, according to the wiki, to be delivered by a TU-160, of which they have many.
However, if you read the wiki or remember the story at the time there was great doubt as to the actual plane and the type of explosive used; it may have been a staged show.
Whatever type of explosive used, it is supposed to be thermobaric, not fuel-air or something like Composition H6, a TNT substitute.
imagine the kick in the arse a Tu crew would get on release of that thing?
both up and forward airspeed
“Some defense analysts question both the yield of the bomb and whether it could be deployed by a Tupolev Tu-160 bomber.
A report by Wired[3] says photos and the video of the event suggest that it is designed to be deployed from the rear of a slow moving cargo plane, and they note that the bomb-test video released by the Russians never shows both the bomb and the bomber in the same camera shot.”
https://en.wikipedia.org/wiki/Father_of_All_Bombs