Although you are likely on a dynamic IP routing configuration, that IP address you receive is usually cached for X period of time (determined by ISP) and then it gets changed.
MAC addresses are more identifiable, but those can be spoofed.
So its a good thing your bank is warning you that "something" happened and its ok to contact them and verify. What is probably more scary is that the banks' security analysis/verification programs haven't made these actions in years past. With all the major hacking account news its about time companies step up their security.
Sort of an associated side-topic: there have been instances where people do report "sluggishness" when accessing the net when it was perfectly fine before. Sometimes its because they dynamically grab a previous user's IP address who was abusing their network (p2p sharing, hacked, ...).
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