Let \({{B_{\ell ,m}}(n)}\) denote the number of \((\ell , m)\) -regular bipartitions of n. We establish some congruence relations for \({{B_{\ell ,m}}(n)}\) by employing the theory of modular forms. For example, let m be a positive integer such that \(m \equiv -1 \pmod 8\) , we find that for all \(n \ge 0\) , the following Ramanujan-type congruences hold: \(\begin{aligned} {{B_{5,m}}\left( {5n + 3} \right) } \equiv 0 \pmod 5. \end{aligned}\) Letting \(p \equiv -1 \pmod {24}\) be a prime, we also prove that for all \(n \ge 0\) and \(k \ge 0\) , \(\begin{aligned} {B_{3,p}}\left( {{p^k}n + \frac{{\left( {p + 1} \right) \left( {{p^k} - 1} \right) }}{{24}}} \right) \equiv {B_{3,p}}(n)\pmod 3. \end{aligned}\)
