She figured the best way to proceed would be to leave the castle immediately, for if someone saw her it wouldn't end well. She would have to prove that she was really innocent, only there weren't many ways to do that. The first option would be to find some verita serum, but that was nearly impossible, especially in these trying times. The second way was to ask the ministry to perform legillimence on her, but this would also bring forth some other crimes she had committed completely unrelated, and they would rather try her for those then admit they had made a mistake. The last, and most promising way was to find out how to prove that her dark mark was fake, and did not bind her, because she had never consented to it. But how...? The dark lord, the one person who could do that, was dead.
Well, she'd figure that out later. Now, first leave this school and find something to eat. She climbed into one of the small boats and made her way out across the lake a last time, only after casting an obscuration charm on her and the boat so she wouldn't be spotted as easily as she would otherwise.
This was a rather relaxing experience, as the boat rowed on its own, slowly parting the glass-like surface of the water. Bellatrix relaxed, letting her patronus slowly fade away, and resting, closing her eyes to just enjoy the calm. The sunlight warmed her face, feeling beautiful after she hadn't been able to experience it for what felt like weeks.
When she arrived in the other side Bella slowly climbed out of the boat stumbling into the water due to her weak state, but that didn't really matter. Her next steps were pretty clear, first she would need somewhere to stay. That already proved difficult, as the only Place she could think of was the family mansion which, she knew for a fact, was being used by the Order, and understandably enough they weren't very fond of her. That meant more hiding, and also maybe robbing a bank or two in order to survive.
The second step was to find someone who could help with her dilemma, but she had no idea who might be able to do that. All her former friends hated her because of the deatheaters and all of her deatheater friends were in prison, dead, or scattered around the world. Then an idea came to her. Of course, she could find Andie! Her sister was the most loving person she had ever met, she would understand. If she was still alive, that is. But still, even on the chance that she wasn't, Bellatrix decided she had to try. Closing her eyes she tried to visualize the Tonks family home from the one time she had been to visit, and with a small pop she apparated away.