It is clear that the relationship between Nick and Jim really mirrors the one between Steph and Babs, right down to Jim cutting in and saying witty lines before Nick has the chance due to "old habits". This is especially prominent when the two of them are out investigating homicidal acts by the villian Livewire on Stephanie's first night out as the official Batgirl.
When Livewire attacked the two cops, Stephanie came to the rescue ,cheerily waving at Nick and shouting "Hey, you!" Gordon acted incredulous at this, and Gage protested, "Nobody bats an eye when you talk to the Batman!". Gordon responded, "I'm pretty sure Batman is legal, Detective."
Stephanie also eavesdropped on Batman and Jim to see what they knew about Francisco Gracia's kidnapping. Stephanie read their lips, but she "has a little fun" and puts in her own "mad-libs" of what they were saying. "He's got loads of enemies, World's Greatest Detective." "But how do we narrow it down to just one, Jim?" "I'm glad we're best friends, Batman." "Me too, chum."
After Steph was successful in taking down the bomber Johnny C, Gordon approached her, which caused her to react with an inward "Holy crap, really?" He shook her hand, telling her he knows she has a rapport of sorts with Gage and congratulating her on a job well done. Steph thought, "Again, holy crap, really?" He began to tell her she reminded him of Barbara, but trailed off before he could finish the sentence. Instead, he told her to be careful. Stephanie is elated to get "props form the freakin' Commissioner!"
Find out more about Jim Gordon here.