  It is known that partial spreads is a class of bent partitions. In
\cite{AM2022Be,MP2021Be}, two classes of bent partitions whose forms are
similar to partial spreads were presented. In \cite{AKM2022Ge}, more bent
partitions $\Gamma_{1}, \Gamma_{2}, \Gamma_{1}^{\bullet}, \Gamma_{2}^{\bullet},
\Theta_{1}, \Theta_{2}$ were presented from (pre)semifields, including the bent
partitions given in \cite{AM2022Be,MP2021Be}. In this paper, we investigate the
relations between bent partitions and vectorial dual-bent functions. For any
prime $p$, we show that one can generate certain bent partitions (called bent
partitions satisfying Condition $\mathcal{C}$) from certain vectorial dual-bent
functions (called vectorial dual-bent functions satisfying Condition A). In
particular, when $p$ is an odd prime, we show that bent partitions satisfying
Condition $\mathcal{C}$ one-to-one correspond to vectorial dual-bent functions
satisfying Condition A. We give an alternative proof that $\Gamma_{1},
\Gamma_{2}, \Gamma_{1}^{\bullet}, \Gamma_{2}^{\bullet}, \Theta_{1}, \Theta_{2}$
are bent partitions. We present a secondary construction of vectorial dual-bent
functions, which can be used to generate more bent partitions. We show that any
ternary weakly regular bent function $f: V_{n}^{(3)}\rightarrow \mathbb{F}_{3}$
($n$ even) of $2$-form can generate a bent partition. When such $f$ is weakly
regular but not regular, the generated bent partition by $f$ is not coming from
a normal bent partition, which answers an open problem proposed in
\cite{AM2022Be}. We give a sufficient condition on constructing partial
difference sets from bent partitions, and when $p$ is an odd prime, we provide
a characterization of bent partitions satisfying Condition $\mathcal{C}$ in
terms of partial difference sets.
