In this article, we report on an experimentally generated soliton and bound-state soliton passively mode-locked erbium-doped fiber laser by incorporating a saturable absorber (SA) made of MoS2/fluorine mica (FM) that was fabricated with the Langmuir–Blodgett (LB) method. The FM substrate is 20 μm thick and easy to bend or cut, like a polymer. However, it has a higher damage threshold and a better thermal dissipation than polymers. In addition, the LB method can be used to fabricate a thin film with good uniformity. In this study, the modulation depth, saturable intensity, and unsaturated loss of the SA are measured as 5.9%, 57.69 MW/cm2, and 13.4%, respectively. Based on the SA, a soliton mode-locked laser is achieved. The pulse duration, repetition rate, and signal-to-noise ratio are 581 fs, 15.67 MHz, and 65 dB, respectively. By adjusting the polarization controller and pump power, we obtain a bound-state soliton mode-locked pulse. The temporal interval between the two solitons forming the bound-state pulse is 2.7 ps. The repetition rate of the bound-state pulses is proportional to the pump power. The maximum repetition rate is 517 MHz, corresponding to the 33rd harmonic of the fundamental repetition rate. The results indicate that the MoS2/FM LB film absorber is a promising photonic device in ultrafast fiber lasers.