As an ISP we need to provide a fully functional nameserver for our customers. So, the only way to do that is to run a separate instance of bind9 on another server as an in-house resolver --- or steal someone else' DNS bandwidth to use them as a resolver.
Bind is not needed for that. In this case you just install a local resolver like dnsmasq and configure mydns to use it.
Take a look at this tutorial:
you have to do just the last step "Installing DNSMasq".