  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
$E_{\mu\nu}$. Focusing on a tachionic potential model, we take a perturbative
approach in the anti-de Sitter (AdS$_5$) background with a single de Sitter
brane. We first formulate the evolution equations for $E_{\mu\nu}$ in the bulk.
Next, applying them to the case of a spatially homogeneous brane, we obtain two
different integral expressions for $E_{\mu\nu}$. 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 $H^2\ell^2\ll1$, where $H$ is the Hubble parameter
on the brane and $\ell$ 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. % atleast on super-Hubble horizon scales. In particular, it is
found that the anticipated non-trivial bulk effect due to the spatially
anisotropic part of $E_{\mu\nu}$ may appear only at %second order in the low
energy expansion, i.e., at $O(H^4\ell^4)$.
