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.