  We prepare mixtures of ultracold CaF molecules and Rb atoms in a magnetic
trap and study their inelastic collisions. When the atoms are prepared in the
spin-stretched state and the molecules in the spin-stretched component of the
first rotationally excited state, they collide inelastically with a rate
coefficient of $k_2 = (6.6 \pm 1.5) \times 10^{-11}$ cm$^{3}$/s at temperatures
near 100~$\mu$K. We attribute this to rotation-changing collisions. When the
molecules are in the ground rotational state we see no inelastic loss and set
an upper bound on the spin relaxation rate coefficient of $k_2 < 5.8 \times
10^{-12}$ cm$^{3}$/s with 95% confidence. We compare these measurements to the
results of a single-channel loss model based on quantum defect theory. The
comparison suggests a short-range loss parameter close to unity for
rotationally excited molecules, but below 0.04 for molecules in the rotational
ground state.
