OK, you have clearly put some effort into trying to resolve this.
Resolving this is really going to all be about properly diagnosing the cause of the problem, so I'll throw some of ideas of things to check at you.
With your virtual adaptor setup in bridged mode your BT virtual machine will attempt to obtain an IP address off a DHCP server on the network that eth0 from your Ubuntu host system is attached to. Is that DHCP server functioning correctly? There is no filtering or other limitations on the use of MAC addresses on your switch is there - since this will involve traffic from two different MAC addresses coming from the same physical host, and MAC filtering on your switch/router would prevent this from working.
What output do you get from the commands 'ifconfig', 'cat /etc/resolv.conf' and 'route' after running '/etc/init.d/networking start'? Do you see evidence of an address being assigned to an interface after running that command? Can you do a DNS query? Can you ping your local default gateway, or the eth0 interface of your Ubuntu host? (Be aware if you have a firewall on your Ubuntu system)
What about performing the same troubleshooting steps after manually assigning details.
Also try capturing packets using Wireshark on your Ubuntu system and on your BT system. What do you see when you try and ping or do lookups from your BT system? What should you see? (Compare with what happens on your Ubuntu box)
What about if you set the network to NAT mode in VirtualBox?