why does edward and bella clink after a while?
I'm assuming you mean click... if that's the case, I think they bond because they're both outsiders. Edward is an outsider in the world of humans and within his own family because he doesn't have a permanent partner. Bella's an outsider, not only because she's new, but because she doesn't necessarily get excited from all of the traditional high school stuff her friends at Forks HS does. They're both lost within their own social clique.
Clink? Maybe you meant click? Bella thinks she has always wanted to be a vampire once she meets Edward and she feels like she doesn't quite fit in. Once Edward comes she falls in love with him and even though she has only known him for less than a year she believes it is true love. Since she doesn't connect with everyone and neither does Edward she believes she loves him and with his family she is happy.
Bella always talks about how she has never fit into the world she was born into, this is another reason why she is so ready to give up her human life for the vampire life. Although she has friends and her parents do love her dearly she has always felt a disconnect with it. Then when Edward comes he present a different world to her where the thoughts of mundane things like having children and marriage are nonexistent and people really get to connect on an emotional level. And these people just so happen to also have a disconnect with the outside world so Bella is basically in heaven.