If you are in a MILP setting, then I think the following should work. Assume $\underline{B},\underline{C}$ and $\overline{B},\overline{C}$ are your respective lower/upper bounds. Then the constraint
$$A \geq \frac{B-C}{\overline{B}-\underline{C}}$$
ensures that $A=1$ if $B-C$ is positive, since the RHS of the equation is between 0 and 1 in this case. When $B-C$ is negative, then the constraint is useless. The constraint
$$\frac{\underline{C}-\overline{B}}{C-B}\geq A$$
ensures that $A=0$ if $B-C$ is negative, for similar reasons.