  Dielectric loss is known to limit state-of-the-art superconducting qubit
lifetimes. Recent experiments imply upper bounds on bulk dielectric loss
tangents on the order of $100$ parts-per-billion, but because these inferences
are drawn from fully fabricated devices with many loss channels, they do not
definitively implicate or exonerate the dielectric. To resolve this ambiguity,
we have devised a measurement method capable of separating and resolving bulk
dielectric loss with a sensitivity at the level of $5$ parts per billion. The
method, which we call the dielectric dipper, involves the in-situ insertion of
a dielectric sample into a high-quality microwave cavity mode. Smoothly varying
the sample's participation in the cavity mode enables a differential
measurement of the sample's dielectric loss tangent. The dielectric dipper can
probe the low-power behavior of dielectrics at cryogenic temperatures, and does
so without the need for any lithographic process, enabling controlled
comparisons of substrate materials and processing techniques. We demonstrate
the method with measurements of EFG sapphire, from which we infer a bulk loss
tangent of $62(7) \times 10^{-9}$ and a substrate-air interface loss tangent of
$12(2) \times 10^{-4}$. For a typical transmon, this bulk loss tangent would
limit device quality factors to less than $20$ million, suggesting that bulk
loss is likely the dominant loss mechanism in the longest-lived transmons on
sapphire. We also demonstrate this method on HEMEX sapphire and bound its bulk
loss tangent to be less than $15(5) \times 10^{-9}$. As this bound is about 3
times smaller than the bulk loss tangent of EFG sapphire, use of HEMEX sapphire
as a substrate would lift the bulk dielectric coherence limit of a typical
transmon qubit to several milliseconds.
