We study the Bernoulli property for a class of partially hyperbolic systems arising from skew products. More precisely, we consider a hyperbolic map
(
T
,
M
,
μ
)
(T,M,\mu )
, where
μ
\mu
is a Gibbs measure, an aperiodic Hölder continuous cocycle
ϕ
:
M
→
R
\phi :M\to \mathbb {R}
with zero mean and a zero-entropy flow
(
K
t
,
N
,
ν
)
(K_t,N,\nu )
. We then study the skew product
T
ϕ
(
x
,
y
)
=
(
T
x
,
K
ϕ
(
x
)
y
)
,
\begin{equation*} T_\phi (x,y)=(Tx,K_{\phi (x)}y), \end{equation*}
acting on
(
M
×
N
,
μ
×
ν
)
(M\times N,\mu \times \nu )
. We show that if
(
K
t
)
(K_t)
is of slow growth and has good equidistribution properties, then
T
ϕ
T_\phi
remains Bernoulli. In particular, our main result applies to
(
K
t
)
(K_t)
being a typical translation flow on a surface of genus
≥
1
\geq 1
or a smooth reparametrization of isometric flows on
T
2
\mathbb {T}^2
. This provides examples of non-algebraic, partially hyperbolic systems which are Bernoulli and for which the center is non-isometric (in fact might be weakly mixing).