The earliest citation I can find for this claim is that it came from a 2007 Bulgarian National Television interview with Andrei Griva, a disciple of Deunov. In that interview, Griva stated this statement could be heard in a radio interview with Einstein broadcast by Radiodiffusion française in 1989. (see comment #2 here, and this newspaper story confirming that 1989 is not a typo) However, Radiodiffusion française ceased to exist in 1949.
More recently, Einstein expert John Norton said he had never come across the name Deunov in all the writings of Einstein that he knew, and that "the whole world bows to me" is not something Einstein would say.
The searchable digital archives of Einstein's papers (which includes not just academic work but also letters, speeches etc) does not contain a document containing Danow (German spelling), Deunov, or Deunoff. If you want you can check other spellings yourself here! https://einsteinpapers.press.princeton.edu/
While it is hard to prove a negative this suggests that the quote is not true. If none of the books cite a source for a quote I would not count them as really reliable sources.