Root cause:
Your home network is using the 192.168.0.0/24 network. That means that your devices in the home network have addresses from 192.168.0.1 (your router) to 192.168.0.254.
Another network somewhere else might/will be using another network range.
Your workstation is presumably configured to use DHCP, i.e. it will get an IP address assigned ot of the network's address range, e.g. 192.168.0.100 at home or 192.168.67.45 somewhere else.
Your VM has a fixed IP out of your home network's range and thus can't connect in a network that uses a different range.
When you switch to the NAT network in Virtualbox, then the same applies. The NAT Network on Virtualbox (which is a network BEHIND your physical adapter provided to the VM) is 10.0.2.0/24 as far as I know and the gateway (your workstation) is 10.0.2.2.
Taking this into consideration, there are multiple possible solutions:
Solution 1: use Bridge and DHCP
You don't specify if you need to use a fixed IP address in the VM. If you don't, then change /etc/network/interfaces to
auto enp0s3
iface enp0s3 inet dhcp
Solution 2: use DHCP and NAT
The same config in your guest like above, but with the NAT network
Solution 3: fixed IP on the NAT network
First use Solution 2.
Then figure out which IP/Subnet you get assigned
then change the config in your /etc/network/interfaces to reflect the changes:
auto enp0s3
iface enp0s3 inet static
address 10.0.2.84
netmask 255.255.255.0
network 10.0.2.0
broadcast 10.0.2.255
gateway 10.0.2.2
dns-nameservers 10.0.2.84 100.100.2.136 100.100.2.138 8.8.8.8 `
You will need to port forward from the outside world to the VM though.
Solution 4: use two network adapters
From your question it is not entirely clear why you are running bind on your VM. I assume you want to use it as a DNS Server for filtering etc in your LAN? If you want to keep your above configuration then just remove the line
gateway 192.168.0.1
and add a second network interface, which might be called enp1s45 for example using dhcp as a gateway to the internet:
auto enp1s45
iface enp1s45 inet dhcp
This way the second interface provides the gateway to the internet. At home your machine will still be 192.168.0.84
