Your router assigns you an IP from a pool of numbers you set, e.g. 1-100. The first computer that connects gets IP 1, the next gets 2, and so on. If address 1 disconnects and a new computer connects, the new computer takes over address 1. If you want your IP to be remembered, make the router reserve it for your network card's MAC address.
BakaBT does not know your internal IP.