Let $B_{s, t}(n)$ denote the number of $(s, t)$-regular bipartitions of $n$. In this paper, we prove several infinite families of congruences modulo $t$ for $B_{s,t}(n)$ where $(s,t)\in\{(2,7),(5^{\beta},7),(3^{\beta},11),(5^{\beta},11),(3^{\beta},17)\}$, $\beta\geq1$.