It's really not surprising that there's a Watcher in Sunnydale. She's been there exactly once before, and didn't do a lot of socializing. He's been surprisingly difficult to get ahold of so far. The only place she's been able to determine he's to be reliably found is the library where he works.
Well, so be it. She'll just have to take extra care not to get blood on the books.
She walks into the library like she has every right to be there, browsing the shelves (genuinely) while keeping half an eye on the man behind the desk.