The correct answer is $\boxed{\text{A}}$.
The first statement is “Some bottles are drinks.” This means that there exists at least one bottle that is also a drink. The second statement is “All drinks are cups.” This means that every drink is a cup.
From the first statement, we can conclude that there exists at least one bottle that is also a cup. This is because the first statement says that some bottles are drinks, and the second statement says that all drinks are cups. Therefore, some bottles must be cups. This is conclusion I.
From the second statement, we can conclude that all cups are drinks. This is because the second statement says that all drinks are cups. Therefore, all cups must be drinks. This is conclusion II.
We cannot conclude that all drinks are bottles, because the first statement only says that some bottles are drinks. It does not say that all bottles are drinks. Therefore, conclusion III does not follow.
We cannot conclude that all cups are bottles, because the first statement only says that some bottles are drinks. It does not say that all bottles are cups. Therefore, conclusion IV does not follow.
Therefore, the only conclusions that follow are I and II.