Quantum steering, a distinctive form of quantum nonlocality with inherent asymmetry, has attracted great interest for its fundamental importance and potential in quantum information processing. This paper investigates the manipulation of quantum steering properties in a cavity Bose-Einstein condensate (BEC) system via single atom doping. The results show that the single-atom-doped cavity BEC system can be exactly mapped to a generalized Dicke model, and both the normal and superradiant phases host rich quantum steering characteristics. In the presence of an impurity atom, only one-way quantum steering exists between the cavity field and the condensate atoms in the normal phase, revealing complete steering asymmetry, while both one-way and two-way quantum steering coexist in the superradiant phase. In stark contrast, without the impurity atom, both one-way and two-way quantum steering appear between the cavity field and the condensate atoms in both the normal and superradiant phases. Remarkably, the single impurity atom can serve as a “single atom switch”for quantum steering: by turning on or off the impurity-BEC interaction, one can flexibly control the direction of one-way steering and realize mutual conversion between one-way and two-way quantum steering. This single-atom switch provides a versatile tool for dynamically manipulating asymmetric quantum correlations. Furthermore, the quantum steering parameter displays an abrupt change precisely at the critical point of the quantum phase transition, serving as an effective indicator to witness the transition between the normal and superradiant phases. These findings provide a new avenue for single-atom control of quantum steering in cavity BEC systems and for probing quantum phase transitions in the generalized Dicke model.