The skills of Occlumency and Legilimency may go hand in hand to a degree, but talent in one does NOT mean one has talent in the other.
Snape's a great Occlumens, but I don't get the impression that he is a particularly good Legilimens. Why?
1)
Snape needed a wand and a verbal spell, at least initially, to perform legilimency on
Harry, but definitely requires eye contact, whereas
Dumbledore, a very good Legilimens, does not necessarily need even eye contact.
2)
Harry is NOT a good Occlumens, which means that probably anyone with any skill at Legilimency, including
Snape, penetrates his defences "with absurd ease".
3) evidently, with only a few months of practice, Draco can prevent
Snape from using Legilimency... either Draco is some kind of prodigy at Occlumency (which is possible, I suppose, given that he doesn't seem to be particularly good at anything else), or that
Snape is not a very good Legilimens at all, at least without a wand.
So perhaps Bellatrix, like
Snape, is a much better Occlumens than Legilimens, and we know she enjoys torture anyway, so it makes sense that she would rather use torture on someone unwilling to volunteer information rather than legilimency (even if she had the skill for it.) It'd be more fun for her that way.
I LOVE the idea that the Longbottoms were tortured for info on the location of the R.A.B. -stolen Horcrux, though! Good one! Maybe Regulus was able to get the locket to the Longbottoms successfully. And if Bellatrix believes she was
Voldemort's "most trusted", then perhaps he WOULD have told her (after killing Regulus) what, exactly, was stolen from him, and ordered her not to share the explicit information of what he was seeking. I'm sure she must have gotten it from them, if they did know (I imagine they must have). Maybe she didn't have time to stash it anywhere safer than that cabinet in the Black family home before the Aurors got her.
Or else Regulus just put the locket in the cabinet, "hidden in plain sight", as it were.