Let $G$ be a topological group acting on a space $X$, what conditions do I need to impose on $G$, $X$ and the action for the map $X\rightarrow X/G$ to be a (Hurewicz) fibration? Moreover, what condition do I need to impose for the map to be a fiber bundle?
I am, in particular, interested in the case when $G$ is $S^1$, $X$ is a non compact space.