He has over 2,500 flight hours in more than 35 different aircraft, and has over 200 carrier landings.

Selected by NASA in January 1990, Bursch became an astronaut in July 1991. His technical assignments to date include: Astronaut Office Operations Development Branch, working on controls and displays for the Space Shuttle and Space Station; Chief of Astronaut Appearances; spacecraft communicator (CAPCOM) in mission control. A veteran of three space flights, Bursch has logged over 746 hours in space. He served as a mission specialist on STS-51 in 1993, STS-68 in 1994 and STS-77 in 1996.

STS-51 launched from the Kennedy Space Center, Florida, on September 12, 1993. During the ten-day mission the crew of five aboard the Shuttle Discovery deployed the U.S. Advanced Communications Technology Satellite (ACTS), and the Shuttle Pallet Satellite (SPAS) with NASA and German scientific experiments aboard. Following a spacewalk by two crew members to evaluate Hubble Space Telescope repair tools, the crew initiated rendezvous burns and Bursch recovered the SPAS using the Remote Manipulator System (RMS). The mission concluded on September 22, 1993, with the first night landing at the Kennedy Space Center. Mission duration was 236 hours and 11 minutes.

STS-68, Space Radar Lab-2 (SRL-2), launched from the Kennedy Space Center, Florida, on September 30, 1994. As part of NASA's Mission to Planet Earth, SRL-2 was the second flight of three advanced radars called SIR-C/X-SAR (Spaceborne Imaging Radar-C/X-Band Synthetic Aperture Radar), and a carbon-monoxide pollution sensor, MAPS (Measurement of Air Pollution from Satellites). SIR-C/X-SAR and MAPS operated together in Endeavour's cargo bay to study Earth's surface and atmosphere, creating radar images of Earth's surface environment and mapping global production and transport of carbon monoxide pollution. Real-time crew observations of environmental conditions, along with over 14,000 photographs aided the science team in interpreting the SRL data. The SRL-2 mission was a highly successful test of technology intended for long-term environmental and geological monitoring of planet Earth. Following 183 orbits of the Earth, the eleven-day mission ended with Space Shuttle Endeavour landing at Edwards Air Force Base, California, on October 11, 1994. Mission duration was 269 hours and 46 minutes.

STS-77 launched from the Kennedy Space Center on May 19, 1996. It included the fourth Spacehab module flight as a scientific laboratory, designated SPACEHAB-4. It consisted of 12 separate materials processing, fluid physics and biotechnology experiments, with an emphasis on commercial space product development. STS-77 completed a record four rendezvous in support of two satellites sponsored by the Goddard Space Flight Center, and the SPARTAN 207/Inflatable Antenna Experiment (IAE) and the Passive Aerodynamically-stabilized Magnetically-damped Satellite/Satellite Test Unit (PAMS/STU). Following 160 orbits of the Earth, the ten-day mission ended with Space Shuttle Endeavour landing at the Kennedy Space Center on May 29, 1996. Mission duration was 240 hours and 39 minutes.