Is a finite regular, bipartite graph (with equal partite sets) always vertex transitive?

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I came across a particular type of graph which is finite, regular and bipartite. I suspect that it is also vertex transitive. Is it true in general?

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I don't believe so. For instance, let $G$ be the disjoint union of even cycles $C_1$ and $C_2$. So we have that $G$ is 2-regular, finite, and bipartite with equal partite sets. However, if $u \in V(C_1)$ and $v \in V(C_2)$ and $|V(C_1)| \neq |V(C_2)|$ then there is no automorphism that takes $u$ to $v$. Perhaps if we require that $G$ be connected then the statement is true.