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Using an improved travelling wave model, we have numerically investigated the dynamics of a Q-switched bismuth-doped fibre laser. Comparison of simulation results with previously reported experimental data demonstrates good agreement of the multipeak lasing structure and the shape of the strongest pulses at various levels of pumping. We have assessed the effect of the main laser parameters on output laser characteristics and quantitatively evaluated the effects of the nonsaturable loss in the active fibre and amplified spontaneous emission on output power saturation. Based on analysis of time-dependent light intensity and gain distributions in the gain medium at different instants in time, we have formulated recommendations how to improve output laser characteristics.