We describe a pulsed positron beam that is optimised for positronium (Ps) laser-spectroscopy experiments. The system is based on a two-stage Surko-type buffer gas trap that produces 4 ns wide pulses containing up to 5 × 105 positrons at a rate of 0.5-10 Hz. By implanting positrons from the trap into a suitable target material, a dilute positronium gas with an initial density of the order of 107 cm−3 is created in vacuum. This is then probed with pulsed (ns) laser systems, where various Ps-laser interactions have been observed via changes in Ps annihilation rates using a fast gamma ray detector. We demonstrate the capabilities of the apparatus and detection methodology via the observation of Rydberg positronium atoms with principal quantum numbers ranging from 11 to 22 and the Stark broadening of the n = 2 → 11 transition in electric fields.