We model the cometary structure around Mira as the interaction of an AGB wind from Mira A, and a streaming environment. Our simulations introduce the following new element: we assume that after 200 kyr of evolution in a dense environment Mira entered the Local Bubble (low density coronal gas). As Mira enters the bubble, the head of the comet expands quite rapidly, while the tail remains well collimated for a 100 kyr timescale. The result is a broad-head/narrow-tail structure that resembles the observed morphology of Miras comet. The simulations were carried out with our new adaptive grid code WALICXE, which is described in detail.