BB84 - Bits needed to detect Eve's presence
Remember that Alice and Bob will only compare those measured qubits that they both measured in the same basis. As you said, on average this will be about 50% of the total qubit stream, but this doesn't actually affect the calculation needed.

As you said, Eve will measure using the wrong basis about 50% of the time. However, even when she does measure using the wrong basis, there is still a 50% chance that Bob receives the correct bit-value. To be explicit, say Alice and Bob decide to compare a qubit after learning they both measured it in the standard basis. Alice had sent Bob a |1> qubit, and Eve then intercepted it, but measured it in the Hadamard basis, yielding either |+> or |->. Finally, Bob measured this state in the standard basis, and will have "correctly" measured |1> about 50% of the time. 

Given that Eve measures in the correct basis and is undetectable 50% of the time, and she measures in the incorrect basis but is still undetectable about 50% of the remaining 50% of the time, it follows that she is only detectable with probability 25% on each compared qubit. So your bounds do indeed hold, if for a slightly different reason.