In the mid-2370s, Admiral Bullock was a role played by a member of Species 8472 in a training simulation on Terrasphere 8, which was designed to accurately simulate Starfleet Headquarters on Earth. "Bullock" was a high-ranking member of Species 8472, who reported directly to "Boothby."
Later, after Species 8472 confirmed that they'd been discovered, "Bullock" reported to "Boothby" that Voyager was approaching, and charged the terrasphere's weapons array. When the two tried searching for a diplomatic answer to the imminent conflict, he was sent, along with "Boothby" and "Valerie Archer". His stance was firmly that the Federation couldn't be trusted, even after "Boothby" had been convinced that they could. After a truce was reached, he had his aide, "Kinis", give Neelix a tour, while he personally showed Tuvok around before Voyager left. (VOY: "In the Flesh")
Admiral Bullock was played by actor Tucker Smallwood.
Smallwood filmed his scenes on Tuesday 7 July 1998, Wednesday 8 July 1998, Thursday 9 July 1998, and Monday 13 July 1998 on Paramount Stages 8 and 16 as well as on location at the Japanese Garden at the Tillman Water Reclamation Plant.
Smallwood's uniform costume was also worn by background actor Adolphus Hankins on Voyager and Ron Blohm on Star Trek: Deep Space Nine and was later sold off on the It's A Wrap! sale and auction on eBay. 
It is unclear if there was a real Starfleet Admiral Bullock or if the persona was created by Species 8472. According to "Boothby" and Kathryn Janeway, the simulation was an incredibly accurate simulacrum of Starfleet Headquarters and its personnel. The Star Trek Encyclopedia (4th ed., vol. 1, p. 109) described the persona created by Species 8472 as a re-creation of Admiral Bullock.
In the game Star Trek Conquest, Bullock was a player character in a reality where the Milky Way Galaxy was embroiled in conflicts between multiple species and cultures. In 2364, Bullock held the rank of commodore and was in command of a fleet during the conflicts. Bullock had an opportunity to be promoted all the way to fleet admiral based on his battle experiences. However, this was at the cost of constant vigilance against the possibility of combat with Klingons, Romulans, Breen, Cardassians, and Jem'Hadar forces, as well as in danger from the Xindi, Ferengi, Orions, and Borg that had taken over the systems that had become neutral as they fell away from the Klingon Empire, Romulan Star Empire, Breen Confederacy, Cardassian Union, and Dominion governments.