Suppose there exists a basis $$B = \left \{ v_{1},...,v_{n}\right \}$$ and basis $$B' = \left \{ v_{1}',...,v_{n}'\right \}$$
Then, if $$\left \langle B,B' \right \rangle=0$$ then B and B' are orthogonal to each other.
What about pairwise orthogonality?
One usually uses "pairwise" when one has a set of more than two different objects. For instance, the vectors $B_1, B_2, B_3, B_4$ are pairwise orthogonal if for any $i \neq j$, we have $\langle B_i, B_j\rangle = 0$, i.e. any pair of vectors from your set is an orthogonal pair. Is that what you're looking for?
Edit I misread the question, thinking $B, B'$ were the vectors, not bases of vector spaces. In this case I would interpret the sentence "$B$ and $B'$ are pairwise orthogonal" as the following: $$ \text{For any } i, j\text{ we have } \langle v_i, v'_j\rangle = 0 $$