  We study the Ricci flow on $\mathbb{R}^{4}$ starting at an
SU(2)-cohomogeneity 1 metric $g_{0}$ whose restriction to any hypersphere is a
Berger metric. We prove that if $g_{0}$ has no necks and is bounded by a
cylinder, then the solution develops a global Type-II singularity and converges
to the Bryant soliton when suitably dilated at the origin. This is the first
example in dimension $n > 3$ of a non-rotationally symmetric Type-II flow
converging to a rotationally symmetric singularity model. Next, we show that if
instead $g_{0}$ has no necks, its curvature decays and the Hopf fibers are not
collapsed, then the solution is immortal. Finally, we prove that if the flow is
Type-I, then there exist minimal 3-spheres for times close to the maximal time.
