Bilger was made a Fellow of the Australian Academy of Technology and Engineering in 1987, and later elected as a Fellow of the Australian Academy of Science in 2003. For outstanding contributions to combustion science, he was awarded the Ya. B. Zeldovich Gold Medal by The Combustion Institute in 1992. Due to the impact of his research and his involvement in the organisation of combustion conferences, the primary keynote lecture during the biannual Australian Combustion Symposium is known as the "Bilger Lecture".