Swipe a conversation partially to the left until you see the Settings icon (shaped like a gear ... whether conversations should appear as bubbles over other apps, for example, change the ...

Tap that icon, and the notification will jump alive ... Tap the chat bubble again, tap “Manage,” then tap “Don’t bubble conversation.” This option will not only dismiss the chat bubble ...

and a preview of the ensuing message will appear in the form of a chat bubble. To unpin a conversation from the top of your messages list, simply long press the large contact icon, then tap Unpin ...