In this paper we study interference management in wireless networks with bursty user traffic. In each time slot, whether a user is on or off for transmission is governed by its own Bernoulli random state. At each transmitter, the states of activities of other users are only available via feedback. We investigate a canonical two-user bursty Gaussian interference channel (IC) with three different feedback models: (1) no feedback, (2) delayed state feedback, and (3) channel output feedback. In all three cases, we characterize the capacity region of the bursty Gaussian IC to within a bounded gap. It turns out that the near-optimal transmit strategies in the non-bursty IC suffice to establish the approximate characterization of capacity in all three cases. In other words, traffic burstiness does not change the high-SNR optimality of the schemes as long as receivers keep track of user activities. Moreover, the capacity region with delayed state feedback is within a bounded gap to that without feedback, and therefore delayed state feedback does not provide significant improvement at high SNR.