Stretching flow problems have several real-world applications in engineering, biological, and industrial fields. The real-world applications of the stretching sheet flow problems are continuous cooling of fiber, manufacturing of rubber and plastics sheets, metal-working processes, crystal growth processes, drawing of the filaments through a quiescent fluid, and consideration of the liquid's films and many others. The present problem focuses on the study of heat and mass transmission phenomena of the magnetohydrodynamics flow of three-dimensional micropolar liquid over a bidirectional stretching surface. In the current analysis, the heat and mass transport mechanism are demonstrated by incorporating the Cattaneo–Christov heat and mass flux model. The micro-organisms are only used to stabilize suspended nanoparticles via bioconvection, which is caused by the combination of magnetic field and a buoyancy force. The current model is demonstrated in the system of higher order partial differential equations (PDEs), which are changed into nonlinear ordinary differential equations (ODEs) by the exploitation of appropriate similarity variables. For the analytical solution, the resulting nonlinear ODEs are simulated by employing the homotopy analysis scheme. The physical significance of velocities, microrotation, temperature, concentration, and micro-organism profiles of the fluid via various embedded parameters are calculated and discussed in a graphical form. The Nusselt number, Sherwood number and micro-organism density number are calculated via tables. Some major findings of the current problem are that the Nusselt number is weakened for the boosted estimation of radiation and thermal relaxation time parameter. The bioconvection Lewis number raised the micro-organism density number. The nanofluid microrotation profile is boosted with the augmentation of the microrotation parameter. The temperature of nanoliquid is lower for thermal relaxation time parameter and nanofluid concentration is lower the for solutal relaxation time parameter.