When Bellatrix found Harry and Hermione, she finds the Sword, and tortures Hermione to see if she took anything out of her Gringotts vault.
Couldn't she have done it 10 times quicker by using Legilimency?
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A couple of reasons spring to mind:
We don’t know that Bellatrix is a Legilimens.
It’s been speculated that she was – as she taught Draco Occlumency, and it would have been useful for practice – but this isn’t confirmed in canon. We do know that it’s quite a tricky branch of magic, and not generally taught. It’s quite plausible she doesn’t know how to do it.
As a corollary, Bellatrix will know that Hermione is an unusually skilled witch. It’s plausible that Hermione is a capable Occlumens, who could fool Bellatrix. Given the gravity of the situation, Bellatrix may prefer to use more tried-and-tested techniques.
Bellatrix has sadistic tendencies.
She often takes pleasure in the suffering and pain of others. Given the choice between extracting truth via tricky magic, and via extreme pain, she’s bound to go for the latter. Cruciatus seems to be her signature spell (see also: Neville’s parents).
Torturing Hermione can help to motivate the others; Legilimency doesn’t.
It’s very obvious that Ron cares about Hermione – he offers to take her place in the interrogation, and can hear her being tortured:
Hermione screamed again from overhead, and they could hear Bellatrix screaming too, but her words were inaudible, for Ron shouted again, “HERMIONE! HERMIONE!”
So if Hermione refuses to talk, Bellatrix can go to Ron instead: tell me what I want to know, and I’ll stop hurting Hermione. Although Harry’s experiences with Legilimency were unpleasant, they weren’t comparable to torture.
I’m sure this technique is a very effective motivator, especially among families. That may lean her towards using torture as an interrogation technique, even if it’s not always optimal.
In addition to the other answers, You don't know how Legilimency works. It may be exceptionally hard mental work. Since Bellatrix is not under any time pressure she may be lazy and use an easy spell rather than exert herself.
Second, Why do you think Legilimency is quick? I don't remember anything in the book to support this, You have to wade through people's memories. That could take hours.
Nobody ever covers Bellatrix as a legillimens, and her abilities as a witch are confined to angry and malevolent spells, never ones of skill or aptitude. The only known and stated legillimens are Voldemort, Snape, and Harry, and potentially Dumbledore if his powers are to be believed, however If he was so powerful why did he need Snape and not Train Harry himself? (if only by his connection to Voldemort) it is not a taught skill, and therefore probably Beyond most witches and wizards of normal intellect's abilities. Those who are capable are powerful, therefore it may be construed that it is a very demanding skill requiring a high level of wizarding ability.
Frm MY reading, limited though it be, Legilimency and Occlumency require concentration and a "calm place" in the wielder, a "receptive place in a calm pool" to sense what either exists in another mind, or to hold a shield against such intrusion. When Harry dropped off the Gringotts dragon, both his calm-place, and his concentration were disturbed, and Voldemort was able to read surface thought from Harry. That, and "the Horcrux he never meant to make" connection between Voldemort and Harry. An automatic resonance. But Hermione had been studying a lot on her own, and was also using the "TIME TURNER" to double up on her courses (including what courses, we have little idea, but both Legilimency and Occlumency could have been included. And Hermione could hold numerous calm-places among the various books and studies.
Bellatrix has no such depth, no "calm-place" nor such a level of concentration to delve to that kind of depth. She is up front and forward, and can only operate on the surface of magic, but with much power. This explains a number of other aspect of her character, and her interactions with other seemingly not so powerful Wizards and Witches.
She forgot. "She was intelligent, but could be easily distracted," it says here.