  Let $ B_{\ell}(n)$ denote the number of $\ell$-regular bipartitions of $n.$
In this article, we prove that $ B_{\ell}(n)$ is always almost divisible by
$p_i^j$ if $p_i^{2a_i}\geq \ell,$ where $j$ is a fixed positive integer and
$\ell=p_1^{a_1}p_2^{a_2}\ldots p_m^{a_m},$ where $p_i$ are prime numbers $\geq
5.$ Further, we obtain an infinities families of congruences for $B_3(n)$ and
$B_5(n)$ by using Hecke eigen form theory and a result of Newman
\cite{Newmann1959}. Furthermore, by applying Radu and Seller's approach, we
obtain an algorithm from which we get several congruences for $B_{p}(n)$, where
$p$ is a prime number.
