The analysis of wind bubbles and superbubbles in Paper I is extended to the case of power-law energy injection [L(in)(t) is-proportional-to t(eta(in)-1)] in a medium with a power-law density distribution [rho(a)(r) is-proportional-to r(-k(rho))]. As before, the wind velocity is assumed to be constant, so that the energy injection rate is proportional to the mass injection rate, L(in)(t) is-proportional-to M(in)(t). The shock in the ambient medium is assumed not to accelerate which requires k(rho) less-than-or-equal-to 3 - eta(in). The evolution is followed from the free-expansion stage, in which the mass of the wind dominates the swept-up mass, through the self-similar stage, to the stage in which the bubble is confined by the pressure of the ambient medium. As in Paper I, winds may be divided into slow and fast, depending on the importance of radiative losses at the transition from the free-expansion to the self-similar stage. Slow winds generally follow the radiative sequence of bubble evolution, which depends on the value of eta(in): At the transition from the free-expansion stage, the bubble is radiative-both the shock in the wind and the shock in the ambient medium are radiative. If eta(in) < (5 - k(rho))/(3 - k(rho)) and if the wind velocity is not too low, the bubble evolves from a radiative bubble to a partially radiative bubble, in which the cooling time of the hot shocked wind is less than the age of the bubble but longer than the crossing time; in this case most of the volume of the bubble is filled by the small fraction of the shocked wind that has not yet cooled. The partially radiative bubble further evolves to an adiabatic bubble if eta(in) < (1 + k(rho))/(2 - k(rho)). The evolution of a bubble blown by a fast wind generally follows the adiabatic sequence of bubble evolution, which does not depend on eta(in), and the shocked wind remains adiabatic unless there is additional mass injection into the bubble. [If the ambient density decreases sufficiently steeply, k(rho) > (14 - 3-eta(in))/(6 + eta(in)); however, slow winds are adiabatic and fast winds are radiative.] Bubbles blown by either slow winds or fast winds eventually expand to the point that the pressure of the ambient medium is significant, and become pressure-confined bubbles. We have obtained characteristic evolutionary time scales, as well as the equation of motion for both the swept-up gas and the wind shock in each evolutionary stage. The special case of a bubble blown in a preexisting wind is discussed in Appendix A. Self-similar bubbles are discussed in Appendix B. If the ambient medium has a finite mass, as in the case of a galactic disk, for example, then the evolution of the bubble is arrested when it reaches a scale height; the possible evolutionary sequences are categorized.
