White dwarfs whose atmospheres are polluted by terrestrial-like planetary debris have become a powerful and unique tool to study evolved planetary systems. This paper presents results for an unbiased Spitzer Infrared Array Camera search for circumstellar dust orbiting a homogeneous and well-defined sample of 134 single white dwarfs. The stars were selected without regard to atmospheric metal content but were chosen to have (1) hydrogen-rich atmospheres, (2) 17000<Teff<25000K and correspondingly young post-main-sequence ages of 15-270Myr, and (3) sufficient far-ultraviolet brightness for a corresponding Hubble Space Telescope COS snapshot. Five white dwarfs were found to host an infrared bright dust disc, three previously known, and two reported here for the first time, yielding a nominal 3.7^+2.4^_-1.0_ percent of white dwarfs in this post-main-sequence age range with detectable circumstellar dust. Remarkably, the complementary Hubble observations indicate that a fraction of 27 percent show metals in their photosphere that can only be explained with ongoing accretion from circumstellar material, indicating that nearly 90 percent of discs escape detection in the infrared, likely due to small emitting surface area. This paper also presents the distribution of disc fractional luminosity as a function of cooling age for all known dusty white dwarfs, suggesting possible disc evolution scenarios and indicating an undetected population of circumstellar discs.