The blood cell most likely to be involved in phagocytosing bacteria at sites of infection is the leukocyte which in blood smears:

The white blood cell(leukocyte)with the largest number of lobes in its nucleus is the neutrophil (also called the polymorphonuclear leukocyte). Mature neutrophils have a minimum of 3 lobes to their nucleus. These cells are specialized for phagocytosis and killing of bacteria and hence this is the correct answer for this question. Ref: Barrett K.E., Barman S.M., Boitano S., Brooks H.L. (2012). Chapter 31. Blood as a Circulatory Fluid & the Dynamics of Blood & Lymph Flow. In K.E. Barrett, S.M. Barman, S. Boitano, H.L. Brooks (Eds), Ganong's Review of Medical Physiology, 24e.