Hitting Time on the Complete Bipartite Graph K₃,₃

Consider the complete bipartite graph $K_{3,3}$ with parts $A = \{a_1, a_2, a_3\}$ and $B = \{b_1, b_2, b_3\}$, where every vertex in $A$ is connected to every vertex in $B$ and vice versa (no edges within a part). A random walk at any vertex moves to each of its $3$ neighbors with equal probability $\tfrac{1}{3}$. Starting from vertex $a_1$, what is the expected number of steps to reach vertex $b_1$ for the first time?