  Ton-scale direct dark matter search experiments should be sensitive to
neutrino-induced recoil events from either $^8$B solar neutrinos or the brief
but intense flux from a core collapse supernova in the Milky Way. These
low-threshold detectors are sensitive to the very low recoil energies, of order
10 keV, deposited via coherent elastic scatters between supernova neutrinos and
target nuclei. Large superheated fluid detectors like PICO-500, a bubble
chamber to be initially filled with an active target of 1 t of C$_3$F$_8$,
should see multiple-bubble events from CE$\nu$NS if the detector is live during
a neutrino burst from a supernova at a distance up to 10 kpc. This paper
discusses conditions under which bubble chambers could be used as an
independent measurement in the event of a supernova similar to SN 1987A, with
particular sensitivity to the currently less-constrained heavy-lepton $\nu_x$
channel.
