Number the variables in a satisfiable formula $B$ as $x_1,x_2,\ldots ,x_n$. Then, for $i=1$ to $n$, consider a version of $B$ that is the formula derived from setting $x_i=1$. If this formula is satisfiable, update $B$ to now be this formula. Otherwise, set $B$ to the formula derived from setting $x_i=0$, and repeat. When we will have iteratively transformed $B$ for each variable, then the remaining formula will just be the constant $1$, and the variables assignments will be a satisfying assignment for the original formula $B$. Note that this algorithm makes $n+1$ calls to the oracle.