If I understand you correctly, you would want to look into something like vpn or ssh and the like.
Many of us you a machine running BT and access said machine with a vpn, or ssh connection, doing so allows what you are asking.
As far as the "define each computer to a set login" part,
Once the machine with BT is running then you would need to use a client to connect to it, doing so of course will cause the BT machine to ask for your login credentials. Since this is a very simple concept and process, there are many guides on the internet to help you. Do have a look.