We consider a braneworld inflation model driven by the dynamics of a scalar field living in the 5-dimensional bulk, the so-called ``bulk inflaton model,'' and investigate the geometry in the bulk and large scale cosmological perturbations on the brane. The bulk gravitational effects on the brane are described by a projection of the 5-dimensional Weyl tensor, which we denote by ${E}_{\ensuremath{\mu}\ensuremath{\nu}}.$ Focusing on a tachyonic potential model, we take a perturbative approach in the anti--de Sitter $({\mathrm{AdS}}_{5})$ background with a single de Sitter brane. We first formulate the evolution equations for ${E}_{\ensuremath{\mu}\ensuremath{\nu}}$ in the bulk. Next, applying them to the case of a spatially homogeneous brane, we obtain two different integral expressions for ${E}_{\ensuremath{\mu}\ensuremath{\nu}}.$ One of them reduces to the expression obtained previously when evaluated on the brane. The other is a new expression that may be useful for analyzing the bulk geometry. Then we consider superhorizon scale cosmological perturbations and evaluate the bulk effects onto the brane. In the limit ${H}^{2}{\mathcal{l}}^{2}\ensuremath{\ll}1,$ where H is the Hubble parameter on the brane and $\mathcal{l}$ is the bulk curvature radius, we find that the effective theory on the brane is identical to the 4-dimensional Einstein-scalar theory with a simple rescaling of the potential even under the presence of inhomogeneities. In particular, it is found that the anticipated nontrivial bulk effect due to the spatially anisotropic part of ${E}_{\ensuremath{\mu}\ensuremath{\nu}}$ may appear only at ${O(H}^{4}{\mathcal{l}}^{4}).$