TL;DR: Throughout the trilogy, Bruce always uses his gravelly voice while in costume, regardless of who he is interacting with.
The circumstances don't seem to make any difference. He might be in the Batcave with Alfred, where no one else can possibly hear him; he'll still speak that way. He might be telling someone who he really is; he'll do it in the Batvoice. No matter who he is speaking to or what else is happening, if he's wearing the Batsuit, he growls everything he says.
When does he use the gravelly voice?
Every time we see him in costume, and a couple of times when he's in street clothes (e.g., when he finds the cops tied up during the funeral procession in The Dark Knight). In short, whenever he is acting as Batman rather than as Bruce Wayne, we hear the voice.
Ra's Al Ghul knew Batman was Bruce, they were alone on a train that was about to blow up, and Ra's was going to blow up with it, but Bruce still used the voice:
Bruce maintains the charade even as he reveals his identity to Rachel:
Bane and Talia know who Batman is, but Bruce keeps up the fake voice:
Lucius built all the Bat-crap and is Bruce's closest confidant aside from Alfred, but Bruce keeps growling anyway:
Alfred wiped Bruce's butt and changed his diapers, he stitches up his Bat-injuries, and he advises him on Bat-tactics; still, Bruce refuses to drop the voice with Alfred:
Batman lets Gordon know his secret identity, still in his gravelly voice:
Here's the kicker: he maintains his fake voice while he is alone and talking to himself! (thanks to Zac Cries for mentioning this one).
Why does he always use his silly voice?
Although it was cut from the film and is therefore probably not canonical, the production notes and a deleted scene say that the voice is a feature of the cowl itself:
Actually, the Batman of "Batman Begins" was designed to sound different from the start. The production notes from the film reveal that Batman's cowl is equipped with mics and speakers (see image above) that allow him to... enhance his speaking voice.
"High-gain stereo microphones are concealed in the ears, allowing Batman to eavesdrop on distant conversations," the notes describe. The mics can also amplify Batman's voice and broadcast it through a discreet speaker in the suit, giving his voice that distinctively gruff, disembodied sound.
While the original script included a scene that went over these Bat-details, mentions of Batman's embedded vocal distorter wound up being cut from the final film. (Still, the Batsuit's tiny speakers remained visible upon close inspection.)
- Yahoo Movies