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How to rapidly disseminate a large-sized file to many recipients in flash crowd arrival patterns is a fundamental challenge in many applications, such as distributing multimedia content. To tackle this challenge, we present the Bee, which is a time-critical peer-to-peer data dissemination system aiming at minimizing the maximum dissemination time for all peers to obtain the complete file in flash crowd arrival patterns. Bee is a decentralized system that organizes peers into a randomized mesh-based overlay, and each peer only works with local knowledge. We introduce the slowest peer first strategy to boost the speed of dissemination and present a topology adaptation algorithm that adapts the number of connections based on upload bandwidth capacity of a peer. Bee is designed to support network heterogeneity and deals with the flash crowd arrival pattern without sacrificing the dissemination speed. We also show the lower bound analysis of the data dissemination problem, and present the experimental results to demonstrate that the performance of Bee can roughly approximate the lower bound of the data dissemination problem under flash crowd traffic.