We describe the design and realization of a scheme for UV laser spectroscopy of singly-ionized iron (Fe II) with very high resolution. A buffer-gas cooled laser ablation source is used to provide a room-temperature plasma with a high density of Fe II. We combine this with a scheme for pulsed-laser saturation spectroscopy to yield sub-Doppler resolution. In a demonstration experiment, we have examined an Fe II transition near 260 nm, attaining a linewidth of about 250 MHz. The method is well suited to measure transition frequencies and hyperfine structure. It could also be used to measure small isotope shifts in isotope-enriched samples.