  We study the boundedness properties of commutators formed by $b$ and $T$,
where $T$ is a bilinear bi-parameter singular integral satisfying natural $T1$
type conditions and $b$ is a little BMO function. For paraproduct free bilinear
bi-parameter singular integrals $T$ we prove that $[b, T]_1 \colon
L^p(\mathbb{R}^{n+m}) \times L^q(\mathbb{R}^{n+m}) \to L^r(\mathbb{R}^{n+m})$
in the full range $1 < p, q \le \infty$, $1/2 < r < \infty$ satisfying $1/p+1/q
= 1/r$. A special case is when $T$ is a bilinear bi-parameter multiplier. We
also prove the corresponding Banach range result for all singular integrals
satisfying the $T1$ type conditions. In doing so we simplify the corresponding
linear proof. Lastly, we prove analogous results for iterated commutators.
