Bulletproof sees me as connected to 192.168.0.4 which I expect.
Right. That's your INTERNAL NETWORK address.
But I'm on 213.107.xx.xxx outwith the router.
Exactly. That's your EXTERNAL address.
The job of the router is to do NETWORK ADDRESS TRANSLATION (NAT) between those two addresses. When you are behind NAT, outside addresses can't see you. In fact, when you're behind a NAT layer like that and you're not opening anything up to the world, your software firewall is probably overkill. But you're about to change that, so it's good you have a software firewall.
Anyhoo, you have to set up port forwarding on that router, or if you really wanted to go all-out, a DMZ. Instructions for doing this should be in the router's manual.