Bellatrix was never really a masochist. Pain was the only constant in her life for such a long time that she clung to it in order to feel secure. She convinced herself that was she positively addicted to pain: anything and anyone that could hurt her. That some combination of torture and poisonous relationships would get her through forth year and whatever catastrophe happened then that she never really told me about. So, she hated pain, but it was all she knew, so she held on to it and craved it and played whatever role she thought was necessary to survive.
She was sadist, yes, I want to deny that but I can't... If she thought someone deserved to suffer, she happily inflicted pain on them. It was much more than that though. Before fourth year, she'd just used simple jinxes on anyone who said something bad about her. But, later, she no longer needed a reason to fight. She punched a fifth year Gryffindor in the face for no apparent reason and I know she'd been practicing Unforgivable Curses on animals and sneaking out after hours to do so. Torture was a vice, an escape, but not a way of life. Everyone thinks that, but it isn't true. I know that because I know her better than anyone. Because I actually care, even if she doesn't.