Summary: We prove a plethora of the boundedness property of Adams type for bilinear fractional integral operators of the form \[ B_{\alpha}(f,g)(x)=\int_{\mathbb{R}^n}\frac{f(x-y)g(x+y)}{|y|^{n-\alpha}}dy,\quad 0<\alpha<n. \] For \(1<t\le s<\infty\), we prove the non-weighted case through the known Adams type result. And we show that these results of Adams type is optimal. For \(0<t\le s<\infty\) and \(0<t\le 1\), we obtain new result of a weighted theory describing Morrey boundedness of above form operators if two weights \((v,\vec{w})\) satisfy \begin{align*} &[v,\vec{w}]_{t,\vec{q}/a}^{r,as}=\mathop{\sup_{Q,Q^{\prime }\in\mathscr{D}}}_{Q\subset Q^{\prime}}\left( \frac{|Q|}{|Q^{\prime }|}\right)^{\frac{1-s}{as}}|Q^{\prime}|^{\frac{1}{r}}\left(\diagup\!\!\!\!\!\!{\int}_Qv^{\frac{t}{1-t}}\right)^{\frac{1-t}{t}}\\&\quad \prod_{i=1}^2\left( \diagup\!\!\!\!\!\!{\int}_{Q^{\prime }}w_i^{-(q_i/a)^{\prime}}\right)^{\frac{1}{(q_i/a)^{\prime}}}<\infty ,\quad 0<t<s<1 \end{align*} and \begin{align*} &[v,\vec{w}]_{t,\vec{q}/{a}}^{r,as}:=\mathop{\sup_{Q,Q^{\prime}\in{\mathscr{D}}}}_{Q\subset Q^{\prime}}\left(\frac{|Q|}{|Q^{\prime}|}\right)^{\frac{1-as}{as}}|Q^{\prime}|^{\frac{1}{r}}\left(\diagup\!\!\!\!\!\!{\int}_Qv^{\frac{t}{1-t}}\right)^{\frac{1-t}{t}}\\&\quad \prod_{i=1}^2\left(\diagup\!\!\!\!\!\!{\int}_{Q^{\prime}}w_i^{-(q_i/a)^{\prime}}\right)^{\frac{1}{(q_i/a)^{\prime}}}<\infty, \quad s\ge 1, \end{align*} where \(\Vert v\Vert_{L^{\infty}(Q)}=\sup_Qv\) when \(t=1, a, r, s, t\) and \(\vec{q}\) satisfy proper conditions. As some applications we formulate a bilinear version of the Olsen inequality, the Fefferman-Stein type dual inequality and the Stein-Weiss inequality on Morrey spaces for fractional integrals.