If you are directly on the path of the information, then there is absolutely nothing preventing you from pretending you are that IP address. If you were the first device along the network that Alice talked with, you could absolutely convince her that you are Bob's IP.
This is a big part of why browsers require signed certificates in order to trust SSL based sites. Without that trusted signed certificate, there is no way to be certain that the server is who they say they are.
As for simply being on the same network, the problem is routers. When you connect to a network, routers need to be informed of what your IP address is so they know in which direction to route those packets. These are formed in to routing tables. Since each IP only has a single record, if another computer claims to be that IP after the first is established, the router simply ignores it as an error and continues routing the way it was going.
You could potentially run in to weird situations where different routers think different network interfaces are the proper IP and based on which direction packets get routed, they could end up in two different places.
Additionally, if you were on an unswitched network that only utilizes hubs (or say, a wireless network with a common key), then it would in fact be possible to intercept traffic bound for another IP address. You wouldn't be able to prevent the other computer from also getting the messages in those cases, so it would be difficult to inject anything for any protocol with a sequence number, but you'd be able to fully monitor it or spoof it entirely if the system wasn't expecting a connection.
In short, the primary problem comes down to the route the data takes. Most modern networks are smart enough to avoid sending data places it doesn't need to go (as this is inefficient). If the network is broadcasting data everywhere, then it becomes far easier, but still with some challenges if you need to prevent the real client from knowing about the tampering (unless you can fully act as gate keeper between them and the rest of the network.)