The well-established Type Ia remnant of Tycho's supernova (SN 1572) reveals discrepant ambient medium density estimates based on either the measured dynamics or on the X-ray emission properties. This discrepancy can potentially be solved by assuming that the supernova remnant (SNR) shock initially moved through a stellar wind bubble, but is currently evolving in the uniform interstellar medium with a relatively low density. We investigate this scenario by combining hydrodynamical simulations of the wind-loss phase and the supernova remnant evolution with a coupled X-ray emission model, which includes non-equilibrium ionization. For the explosion models we use the well-known W7 deflagration model and the delayed detonation model that was previously shown to provide good fits to the X-ray emission of Tycho's SNR. Our simulations confirm that a uniform ambient density cannot simultaneously reproduce the dynamical and X-ray emission properties of Tycho. In contrast, models that considered that the remnant was evolving in a dense, but small, wind bubble reproduce reasonably well both the measured X-ray emission spectrum and the expansion parameter of Tycho's SNR. Finally, we discuss possible mass loss scenarios in the context of single- and double-degenerate models which possible could form such a small dense wind bubble. ; Comment: 12 pages, 7 figures, accepted for publication in MNRAS