A Randall-Sundrum-type brane-cosmological model in which slow-roll inflation on the brane is driven solely by a bulk scalar field was recently proposed by Himemoto and Sasaki. We analyze their model in detail and calculate the quantum fluctuations of the bulk scalar field $\phi$ with $m^2{=V}^{″}\left(\phi \right).\mathrm{}$ We decompose the bulk scalar field into the infinite mass spectrum of four-dimensional fields; the field with the smallest mass square, called the zero mode, and the Kaluza-Klein modes above it with a mass gap. We find the zero-mode dominance of the classical solution holds if $|m^2|{\overline{l}}^2\ll 1,$ where $\overline{l}$ is the curvature radius of the effectively anti–de Sitter bulk, but it is violated if $|m^2|{\overline{l}}^2\gg 1,$ though the violation is very small. Then we evaluate the vacuum expectation value $〈\delta {\phi }^2〉$ on the brane. We find the zero-mode contribution completely dominates if $|m^2|{\overline{l}}^2\ll 1,$ similar to the case of classical background. In contrast, we find the Kaluza-Klein contribution is small but non-negligible if the value of $|m^2|{\overline{l}}^2$ is large.

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