OK... but the behavior you described appears to be a timeout issue -- and we can demonstrate (by running dig and host commands on the BIND server) that the timeouts are not coming from the "Internal DNS Server <=> Outside DNS servers" interface, so the problem appears to be between your workstation (local client) and the BIND server (local DNS server).
Have you tried resetting /etc/resolv.conf on the Linux workstation to point to a public DNS server? (Say, 4.2.2.2). It is possible your Linux Workstation is having more than just DNS network issues!
Than again, looking at your original post -- it is also possible that you're exceeding the number of active, simultaneous IP connections you're allowed -- either in your local Linux workstation, or (most likely) your local router, or (less likely) the remote web server.
Do you have the same problem on ALL websites, or just a select few (which may have a larger than normal number of components).
Just call me Curious
Dan
IT4SOHO