Summary: Let \(f:A\rightarrow B\) and \(g:A \rightarrow C\) be two ring homomorphisms and let \(J\) and \(J'\) be two ideals of \(B\) and \(C\), respectively, such that \(f^{-1}(J)=g^{-1}(J')\). The bi-amalgamation of \(A\) with \((B,C)\) along \((J,J')\) with respect of \((f,g)\) is the subring of \(B\times C\) given by \[ A\bowtie^{f,g}(J,J')=\{(f(a)+j,g(a)+j')/a \in A, (j,j') \in J\times J'\}. \] In this paper, we study the transference of \(pm^+\), \(pm\) and finite character ring-properties in the bi-amalgamation.