In this study, in a bio-hybrid microswimmer system driven by multiple Serratia marcescens bacteria, we quantify the chemotactic drift of a large number of microswimmers towards L-serine and elucidate the associated collective chemotaxis behavior by statistical analysis of over a thousand swimming trajectories of the microswimmers. The results show that the microswimmers have a strong heading preference for moving up the L-serine gradient, while their speed does not change considerably when moving up and down the gradient; therefore, the heading bias constitutes the major factor that produces the chemotactic drift. The heading direction of a microswimmer is found to be significantly more persistent when it moves up the L-serine gradient than when it travels down the gradient; this effect causes the apparent heading preference of the microswimmers and is the crucial reason that enables the seemingly cooperative chemotaxis of multiple bacteria on a microswimmer. In addition, we find that their chemotactic drift velocity increases superquadratically with their mean swimming speed, suggesting that chemotaxis of bio-hybrid microsystems can be enhanced by designing and building faster microswimmers. Such bio-hybrid microswimmers with chemotactic steering capability may find future applications in targeted drug delivery, bioengineering, and lab-on-a-chip devices.