It sounds like you went about those calculations by deciding on a result and then looking to fill those slots. That's not really the best way to evaluate things like this. If you look at the wiki article that discusses Bismarck's actual quote, it argues that it's quite false.
Great power - Wikipedia, the free encyclopedia
In 1900, there were 8 great powers. In 1939, there were 7. In 2000, there were 7.
It's quite possible to always come up with a list of the "top 5" powers and call that the great powers. That doesn't mean that each of those five powers are closer to each other than the fifth power is to the next greatest. I think you'd have a very hard time proving that.
Even if you're right that the US and China would be defeated (which I very much doubt), you acknowledge that the US/USSR would have defeated the other three, thus disproving Bismarck's theory (if it was ever really a theory).
I said that was the only conceivable situation where I could imagine Bismarck's theory being upset -- but alas, there is always the unwritten clauses of a theory that make it so applicable. I would argue that a good addition to Bismarck's theory would be a clause stating that, in general, the two most powerful nations of the time aren't usually on the same side, thus precluding the possibility of a USSR/USA alliance.
At any rate, I've seen that wikipedia article many a time, and I don't really know where you got the bit about Bismarck saying the exact opposite of his own theory. Seems a bit daft...
At any rate, that chart with all the great powers? Take a look at the trends, one more time -- watch how, whenever there are challengers to the original five, like, say, in 1914 Italy trying to muscle its way in -- history promptly rights itself by starting a massive power and reducing at least some of the nations contending for dominance, until there are only... Huh, five left!
At any rate, on a less abstract note, why exactly do you believe a Chinese-American alliance would overcome Russia, Britain and France? China's only hope to survive such a war would be a massive, pre-emptive strike on their closest foe... Which would be Russia. They have little to no naval capabilities, and as shown in every war China's been in in the last century, their entire strategy centres on sending as many people to the front as possible. So, without naval capabilities, they're force to attempt to invade Siberia (which always goes well), with an army that's already known for its supply logistic problems (AKA getting food and appropriate gear to their troops).
The States, on the other hand, would be more of a problem -- the States have a large and modern army, if a bit ill-trained, but they absolutely have the transport capabilities that the Chinese lack. Even so, a defensive action on Europe's part would almost conclusively end in American repulsion, when considering the scenarios of the most recent major wars in Europe. Attempting to make landfall in either Britain or France would be disastrously stupid -- the only reason Normandy was a success was because Hitler wouldn't listen to Rommel's pleas to pull troops from the Eastern Front to defend France.
Furthermore, on the defensive, Britain's got to have the single best alliance network on Earth. They're a part of the EU, which has a military clause, as well as the Commonwealth, which has a military clause, and NATO, which is at its heart a military alliance. An attack on Britain by the States would arouse the support of France, Germany and Italy, if not the rest of the EU, as well as the ire of Canada, South Africa, India and (perhaps) Pakistan. The NATO clause would most likely be destroyed entirely, as one NATO nation attacking another would probably render the alliance void -- but it can be assured that an aggressive US wouldn't receive support from anyone outside of Israel.
In short, even though this is a ridiculous debate to have in the first place, I can't foresee a Chinese-American alliance succeeding against a British-French-Russian alliance any time in the foreseeable future.
