A map $f: X\to S$ is called evenly submersive if each $s\in S$ has a neighborhood $W$ such that $p^{-1}W$ is covered by open sets $U\subset X$ diffeomorphic to $V\times W$ with $V$ open in $X_s$, and such that $p$ restricted to $U$ coincides with projection onto the second factor.

What is an example of an evenly submersive map that is not a fiber bundle? In what way do evenly submersive maps differ from fiber bundles?