I'll admit I have no real defense for this character. She seems to be pitiless, ruthless, cold, sadistic, maniacal...
I believe Bella to be a power-hungry character. She is the oldest of her sisters; independent, sharp witted, and even potentially something of a control freak. She feels some need for control over her youngest sister, Narcissa. I think that she fears that Narcissa will also "betray her" and her cause, similarly to how Andromeda did. Why does this matter to Bellatrix? Because if both her sisters leave her and her cause, there will be an inkling of doubt within her... she will realize that she is not in control, and that she has done something wrong- By this "I've done something wrong" I mean more "I've made someone who matters to me unhappy, I don't like this situation." It's a kind of empty apology regret, a band-aid to cover a scar. She may be sorry for having them gone, or for upsetting them, if anything. When Andromeda married Ted Tonks, I suspect Bella felt angry and betrayed. Everything she had ever known, ever been taught... Andromeda had essentially spit on it. Bellatrix would not try to understand her younger sister though. Keep in mind- Andromeda is her younger sister. Bellatrix is oldest. Partially due to this, I think, Bella believes that she knows best. She is the oldest, the most experienced, and her sisters should be looking to her as an example. And when she is not in control... She is upset.
So... Bellatrix being a control freak... Thoughts, anyone?