William Hall Bush was born in Manhattan, New York City,[2] the son of Josephine (née Bradley) and Jonathan Bush, whose older brother George H. W. Bush was the 41st U.S. president.
Source: wikipedia.
Cousin to W. and Jeb.
seems like uncle Billy to W and Jeb, since your source said Billy Bush is the brother of W and Jeb’s Father, GHW Bush.