  We estimate the $3$-colour bipartite Ramsey number for balanced bipartite
graphs $H$ with small bandwidth and bounded maximum degree. More precisely, we
show that the minimum value of $N$ such that in any $3$-edge colouring of
$K_{N,N}$ there is a monochromatic copy of $H$ is at most
$\big(3/2+o(1)\big)|V(H)|$. In particular, we determine asymptotically the
$3$-colour bipartite Ramsey number for balanced grid graphs.
