Bus 397 is operated by Connexxion (but to make things more confusing, the buses have the red “R-Net” livery that is shared between several operators and not the white/green livery of regular Connexxion buses).
The description of the Amsterdam Travel Ticket on the GVB website seems a little more specific:
The Amsterdam Travel Ticket provides unlimited travel on the train (NS railway), the Amsterdam Airport Express (bus 397) and Niteliner N97 (of Connexxion) between Schiphol and Amsterdam and unlimited travel for all GVB trams, day buses, night buses and metros.
Hard to say for sure but seems to confirm that only travel between the airport and Amsterdam is included. Unlimited travel on other routes is only for GVB buses.
To pay for additional stations, you can just tap a pay-as-you-go transit card, a debit card or a credit card when you reach the end of the coverage area, as you would do when getting on the bus at that station. In buses and trams, you will find card readers at every door and every card reader can be used to tap in or out (i.e. even if the door is marked as an exit door, you can still tap in) so you don't need to walk off the bus or go all the way to the front. Do not forget to tap out when exiting the bus!
You will however be charged for the full price of a trip from, say, Schiphol to Nieuw Vennep, including a fixed €1.08 boarding fee (basistarief) and not merely some “top-up fare” that would only be valid together with your day card.