Figure-nine fiber lasers can realize all-polarization-maintaining, self-started, highly stable mode-locked laser sources, and are very attractive for applications such as optical frequency combs, metrology, etc. In this work, we investigated a dispersion-managed, polarization-maintaining, Er-doped, ultrashort-pulse figure-nine fiber laser both experimentally and numerically. Stable, self-started, passive mode-locking operation was achieved in a wide net cavity dispersion region, covering the soliton, stretched pulse, and dissipative soliton mode-locking regimes. A 132 fs ultrashort pulse with spectral width of 46 nm was obtained in the stretched pulse mode-locking regime. The initial mode-locking process and dynamics inside the cavity, in addition to the fundamental characteristics of the output pulses, were examined via numerical analysis. Owing to the asymmetric configuration, the propagation behaviors were different between the two counter-propagation directions. It was found that a large breathing had already started before the passive mode-locking point in stretched pulse mode-locking operation. Intense overshoots were also observed at the beginning of passive mode-locking. Numerical results were almost in agreement with the experimental ones.