*sighs* I wish I had a scan on hand, but he did welcome her to the batcave. That was where he welcomed Steph back and in front of Alfred to boot. So, no. I don't think it's a stretch to think Steph is allowed to work in the batcave with or without him there.
Granted, I'm not sure which batcave is being used, not denying that Barbara couldn't have come up with a better "batgirl cave" herself, but in this case I'll have to blame editorial for this fuck up. You're not the only one wondering how that lapse in continuity happened. I'm mostly frustrated that DC editorial once more forgot to connect their books and let their writers know what's going on in the other books.
That said, I don't believe the analogy with Huntress works. Oracle may not have been there often or physically, but she still assisted Batman more than enough in the past (much more than Huntress did). So much that he saw the need to wean himself off her help when she and the BOP left Gotham City. Meaning, it's not a stretch to think Babs can have access to the tools his batcave offers, because to not do so would make him all kinds of a selfish ungrateful bastard.
And seriously...if they have Bruce have a bitchfest because Steph and Babs are operating out of his batcave when he comes back, I'm going to have a bitchfest on DC editorial for not doing their goddamn job and keeping the writers updated to what's "kosher" for each character to do or not do. How petty. Babs and Steph are fighting crime, they're not having a slumber party. As long as they aren't endangering Bruce's identity or his other toys which supposedly Dick stored away...and doesn't seem to be the case, I don't see what the problem is. (unless this is going to be a plotpoint in the future...ugh)
I do believe they have just as much as right as Dick Grayson does to use or NOT use the batcave...mostly because Batman NEVER prohibited Steph from the batcave and mostly because Babs helped him tons in the past, probably just as much as Dick Grayson did.
By the time Bruce comes back, Babs and Steph probably will have another place to operate out of, because DC's gotta keep all their books fresh when the big guy returns.