A stable passive Q-switched ytterbium-doped fiber laser (YDFL) operating at 1057.4 and 1044.5 nm is demonstrated using two types of topological insulator-based saturable absorbers (SAs): bismuth (III) selenide (Bi2Se3) and bismuth (III) telluride (Bi2Te3). These materials are embedded in polyvinyl alcohol film and incorporated in the YDFL cavity. Using Bi2Se3 SA, the YDFL obtains a stable train of pulses with a repetition rate that is tunable from 48.83 to 102 kHz. Meanwhile, the corresponding pulse width decreases from 8.9 to 3.48 μs as the pump power increases from 67.6 to 88.3 mW. For the Bi2Te3-based Q-switched YDFL, the repetition rate grows from 43.25 to 93.63 kHz and the pulse width shrinks from 5.65 to 2.01 μs as the 980-nm pump power rises from 72.8 to 98.4 mW. The maximum pulse energy is obtained with the Bi2Te3 SA at 29.95 nJ.