Let $b_l (n)$ denote the number of $l$-regular partitions of $n$ and $B_l (n)$ denote the number of $l$-regular bipartitions of $n$. In this paper, we establish several infinite families of congruences satisfied by $B_l (n)$ for $l \in {2, 4, 7}$. We also establish a relation between $b_9 (2n)$ and $B_3 (n)$.