  The notion of the circular coloring of signed graphs is a recent one that
simultaneously extends both notions of the circular coloring of graphs and
$0$-free coloring of signed graphs. A circular $r$-coloring of a signed graph
$(G, \sigma)$ is to assign points of a circle of circumference $r$, $r\geq 2$,
to the vertices of $G$ such that vertices connected by a positive edge are at
circular distance at least $1$ and vertices connected by a negative edge are at
circular distance at most $\frac{r}{2}-1$. The infimum of all $r$ for which
$(G, \sigma)$ admits a circular $r$-coloring is said to be the circular
chromatic number of $(G, \sigma)$ and is denoted by $\chi_c(G, \sigma)$. For
any rational number $r=\frac{p}{q}$, two notions of circular cliques are
presented corresponding to the edge-sign preserving homomorphism and the
switching homomorphism.
  It is also shown that the restriction of the study of circular chromatic
numbers to the class of signed bipartite simple graphs already captures the
study of circular chromatic numbers of graphs via basic graph operations, even
though the circular chromatic number of every signed bipartite graph is bounded
above by $4$.
  In this work, we consider the restriction of the circular chromatic number to
this class of signed graphs and construct signed bipartite circular cliques
with respect to both notions of homomorphisms. We then present reformulations
of the $4$-Color Theorem and the Gr\"otzsch theorem. As a bipartite analogue of
Gr\"otzsch's theorem, we prove that every signed bipartite planar graph of
negative girth at least $6$ has circular chromatic number at most $3$.
