A Pensacola judge who sentenced Hill is the fourth person to receive one of the letters, reportedly containing a .270-caliber rifle bullet.
Hill fatally shot an abortion doctor and his bodyguard in 1994.
The other threatening letters were sent to Florida Attorney General Charlie Crist, Corrections Secretary James Crosby and Florida State Prison Warden Joe Thompson. Those letters also contained bullets.
Bush rejected the notion that Hill was acting in the name of God and should be spared execution next month.
Bush says, "This man brutally murdered people, cold-blooded, premeditated. To do it for life's sake makes it even sicker in my opinion.''
A published report from The Miami Herald says that the letters denounce "baby killing'' and say officials are going to be held responsible for them.
One source says at least one of the letters also made a threat against Gov. Bush, who signed a death warrant for Hill in July.
Bush says he has no plans to stop the execution.
Viewers with disabilities can get assistance accessing this station's FCC Public Inspection File by contacting the station with the information listed below. Questions or concerns relating to the accessibility of the FCC's online public file system should be directed to the FCC at 888-225-5322, 888-835-5322 (TTY), or firstname.lastname@example.org.