A ring \(R\) is strongly \(\pi\)-regular, if for each \(a\in R\) there exists a positive integer \(m=m(a)\) such that \(a^mR=a^{m+1}R\). A ring \(R\) is of bounded index, if there exists a positive integer \(n\) such that \(a^n=0\) for all nilpotent \(a\in R\). The main result is the following. Let \(T\) be the ring of Morita context \((A,B,M,N,\psi,\varphi)\) with zero pairings \(\psi\) and \(\varphi\). Then \(T\) is strongly \(\pi\)-regular of bounded index if and only if so are the rings \(A\) and \(B\). Similar results are obtained for strongly \(\pi\)-regular rings with nilpotent Jacobson radical and also for right (left) quasi-duo strongly \(\pi\)-regular rings.