The shallow potential wells of star-forming dwarf galaxies make their surrounding circumgalactic and intergalactic medium (CGM/IGM) sensitive laboratories for studying the inflows and outflows thought to regulate galaxy evolution. We present new absorption-line measurements in quasar sightlines probing within projected distances of $<300$ kpc from 91 star-forming field dwarf galaxies with a median stellar mass of $\log{M_\star/\rm{M_\odot}} \approx 8.3$ at $0.077 < z < 0.73$ from the Cosmic Ultraviolet Baryon Survey (CUBS). In this redshift range, the CUBS quasar spectra cover a suite of transitions including H I, low and intermediate metal ions (e.g., C II, Si II, C III, and Si III), and highly ionized O VI. This CUBS-Dwarfs survey enables constraints with samples 9$\times$ larger than past dwarf CGM/IGM studies with similar ionic coverage. We find that low and intermediate ionization metal absorption is rare around dwarf galaxies, consistent with previous surveys of local dwarfs. In contrast, highly ionized O VI is commonly observed in sightlines that pass within the virial radius of a dwarf, and O VI detection rates are non-negligible at projected distances of 1$-$2$\times$ the virial radius. Based on these measurements, we estimate that the O VI-bearing phase of the CGM/IGM accounts for a dominant share of the metal budget of dwarf galaxies. The absorption kinematics suggest that a relatively modest fraction of the O VI-bearing gas is formally unbound. Together, these results imply that low-mass systems at $z\lesssim 1$ effectively retain a substantial fraction of their metals within the nearby CGM and IGM.