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Actin polymerization driven stochastic movement of the bacteria Listeria monocytogenes is often measured using single-particle tracking (SPT) methodology and analyzed in terms of statistics. Experimental results suggested a dynamic association between the growing actin filaments and the propelled bacteria. Based on an alternative mathematical formalism for a Brownian ratchet (BR), we introduce such an attractive interaction into the one-dimensional BR model and show that its effect is equivalent to an external resistant force on the bacterium. Such a force significantly reduces the Brownian motion of a driven bacterium, and accentuates the stepping due to polymerization. We then consider the growth, with and without a barrier, of a filamentous bundle consisting of N identical filaments. It is shown that the bundle grows with a similar rate as a single filament in the absence of a load, but can oppose N times the external force under the stalling condition. A set of relationships describing the velocity of the bacterium movement (V_z) and its apparent diffusivity (D_z) as functions of the resistant force (F) and the number of filaments in a bundle (N) are obtained. The theoretical study suggests methods for data analysis in future experiments with applied external resistant force.