Greyhound's website is definitely a safe way to go. Its safe and secure, and as far as worrying about a ticket not being valid when you show up... Do you figure they are a two bit company? No, they are the biggest and most recognizable bus company across North America.

As far as the way to go, I recently took a Quick Shuttle for around 45 bucks, which makes several pick ups around Vancouver and South Surrey on its way to the border, makes a few stops at Bellingham Airport and the Outlet Malls and then stops Downtown Seattle and SeaTac. Great value. Free WiFi and all that.