  We provide the first solution to the problem of counting rooted 3-connected
bipartite planar maps. Our starting point is the enumeration of bicoloured
planar maps according to the number of edges and monochromatic edges, following
Bernardi and Bousquet-M\'elou [J. Comb. Theory Ser. B, 101 (2011), 315-377].
The decomposition of a map into 2- and 3-connected components allows us to
obtain the generating functions of 2-and 3-connected bicoloured maps. Setting
to zero the variable marking monochromatic edges we obtain the generating
function of 3-connected bipartite maps, which is algebraic of degree 26. We
deduce from it an asymptotic estimate for the number of 3-connected bipartite
planar maps of the form $t \cdot n^{-5/2} \gamma^n$, where $\gamma=\rho^{-1}
\approx 2.40958$ and $\rho \approx 0.41501$ is an algebraic number of degree
10.
