For the moment, Buffy wasn't thinking about anything but kicking some vampire ass and making sure Cordelia got back home safely. She also didn't want anyone but the baddies dying, but other than that, she didn't really care how the whole thing went down. It was very difficult for her to give up her previous leadership position, especially to someone who had known so little about it all when he first became the Champion. Buffy didn't much care for titles, and she didn't much care for the situation as a whole, but it wasn't top priority just then.
The teleportation was an odd process, but Buffy had experienced stranger things in her lifetime, so she didn't say anything about it once she and Peter both appeared inside a house that was quiet and still the one minute, and then being bombarded by vamps the next.
"Not a problem," Buffy replied matter-of-factly, taking out her stake and ramming it into an approaching vampire's chest, causing him to explode in a cloud of dust before a second took his place. "I don't mind think anyone's gonna mind."