Combining 2 problems in NP into one
There are at least two ways to do it. The first is to take a disjoint sum of $B$ and $C$, which can be done in many ways, for example
$$
\{0x : x \in B\} \cup \{1y : y \in C\}.
$$
The second is to use an NP-complete language $L$ as an oracle. Since any problem in NP reduces to $L$ in polynomial time, you can simulate a $B$-oracle using an $L$-oracle.