Not Ulysses...
After the end of the Trojan War, on his protracted voyage back home to the island of Ithaca, Ulysses does go to "hell," i.e. the land of the dead. His adventure there is narrated in the Odyssey, wherein his Greek name Odysseus is used, and in which he takes a tour of the Underworld, which includes vistas of certain sinners suffering in Tartarus, the deepest part of the netherworld.
During this hell-tour, Odysseus meets the shades (or ghosts) of several people he had known before they died, but his mission of going to hell is in order to acquire directions home from the dead prophet Teiresias, not to save anyone. He doesn't have a girlfriend at this point, since the main motivation for his voyage is to get back home to his wife Penelope.
... But Orpheus
The story you are asking about must be the myth of Orpheus and Eurydice, who lived a generation earlier than Ulysses/Odysseus. Orpheus was a musician whose song was so beautiful that it had the power to charm all those who listened to it, including plants and rivers, the sea, and even ferocious beasts.
He was married to Eurydice who died of a snakebite. When this happened, he undertook a journey to the Underworld in order to bring her back to life. Using his magical music he was able to bypass all the security features of the realm, including Cerberus, the monstrous triple-headed watchdog who guarded the entrance.
Upon gaining an audience with Hades and Persephone, the deities who ruled over the dead, he managed to convince them to let her go so that she might live again. This, however, was granted with the condition that on the way out of the Underworld, Eurydice would follow behind Orpheus and he could lay eyes upon her only once they had emerged back into the upper world.
If he failed to observe this protocol, she would remain dead. So the two of them began their trip out of the realm of Hades, and they were just beginning to rise back out into the land of the living when Orpheus, in a moment of doubt about whether he might be being tricked and that his wife might not actually be behind him at all, took a quick glance back to make sure. He saw that she was in fact there, but now she instantly got sucked back down into the house of Hades.
He tried to repeat his infiltration of the Underworld, but this time found no access whatsoever, and he shortly afterwards died a tragic death in misery, pining over his wife whom he had lost twice over.
Further Reading: The Greek Mythology Link article on Orpheus
