Spread and partial spread constructions are the most powerful bent function constructions. A large variety of bent functions from a 2m-dimensional vector space $${\mathbb {V}}_{2m}^{(p)}$$ over $${\mathbb {F}}_p$$ into $${\mathbb {F}}_p$$ can be generated, which are constant on the sets of a partition of $${\mathbb {V}}_{2m}^{(p)}$$ obtained with the subspaces of the (partial) spread. Moreover, from spreads one obtains not only bent functions between elementary abelian groups, but bent functions from $${\mathbb {V}}_{2m}^{(p)}$$ to B, where B can be any abelian group of order $$p^k$$ , $$k\le m$$ . As recently shown (Meidl, Pirsic 2021), partitions from spreads are not the only partitions of $${\mathbb {V}}_{2m}^{(2)}$$ , with these remarkable properties. In this article we present first such partitions—other than (partial) spreads—which we call bent partitions, for $${\mathbb {V}}_{2m}^{(p)}$$ , p odd. We investigate general properties of bent partitions, like number and cardinality of the subsets of the partition. We show that with bent partitions we can construct bent functions from $${\mathbb {V}}_{2m}^{(p)}$$ into a cyclic group $${\mathbb {Z}}_{p^k}$$ . With these results, we obtain the first constructions of bent functions from $${\mathbb {V}}_{2m}^{(p)}$$ into $${\mathbb {Z}}_{p^k}$$ , p odd, which provably do not come from (partial) spreads.