This research addresses the interesting rheological features of Jeffrey nanofluid containing gyrotactic microorganism over an accelerated configuration. The additional consequences of activation energy and thermal radiation are also encountered in the current flow problem. The characteristics of nanofluid is utilized by using Buongiorno’s nanofluid model, while the phenomenon of bioconvection is evaluated by Kuznestov and Nield model. Unlike traditional attempts, the analysis for thermal radiation is performed by using “one parametric approach” by expressing the Prandtl number and thermal radiation parameter in combined form, namely, effective Prandtl number. The governing equations reflecting the flow problem are analytically treated with the help of homotopic algorithm. The impact of flow parameters is graphically elaborated with relevant physical significance. Further, the numerical expressions for effective local Nusselt number, local Sherwood number, and motile density number with variation of flow parameters in articulated tabular form. It is observed that magnitude of skin friction coefficient oscillates periodically with time and magnitude of oscillation increases with increment of Deborah number and mixed convection constant. It is further emphasized that the temperature distribution is enhanced with buoyancy ratio constant and bioconvection Rayleigh number. The microorganism distribution increases with buoyancy ratio constant but reverse trend has been examined for Peclet number. The observations from the reported problem can be more effective for the development of bifurcation processes, biofuels, enzymes, etc.