When Rush found the bridge, the hallucination of Gloria appeared to him, aware that he had no intention of revealing his discovery to the rest of the crew. She seems to exist to second-guess Rush's decisions, as well as recommend that he take care of himself. She is unhelpful with scientific matters, and ignores Rush's requests to let him speak to the hallucination of Jeremy Franklin. (SGU: "Aftermath", "Awakening", "Pathogen")
With the recent discovery that the Jeremy Franklin 'hallucination' is actually the remnants of Franklin's consciousness that were uploaded into Destiny's database when he used the interface chair (SGU: "Hope"), it is unclear whether Destiny was able to create the Gloria hallucination based on the memories it acquired from Rush during his own experience in the chair or if—given the more personal advice she offers Rush—she is just a conventional hallucination. It would be reasonable to assume she's an avatar created by Destiny since the only instances of crew members legitimately hallucinating were caused by the alien tick that had attached itself to members of an away team. In all other instances, Destiny has manufactured avatars and full simulations through it's ability to manipulate brain waves.
This notion is further bolstered by the fact that Gloria's comments seem to simply reflect Dr. Rush's memories of her (comments about him and his personality, memories of them together, etc), while those whom are known to have actually uploaded their consciousnesses to the ship like Jeremy Franklin, Ginn, and Amanda Perry are all clearly sentient and functioning independently of Destiny's AI and simply have the depth and breadth of Destiny's vast knowledge available to them.