Already as a student Bilger joined the Young Union in 1996 and was also a member of the CDU. From 1998 to 1999 he served as chairman of the Baden-Württemberg Land branch of the Pupils' Union and from 1998 to 2000 as federal managing director of the Pupil Union Germany. In 2006, Bilger was elected chairman of the Junge Union Baden-Württemberg and was confirmed in office in the years 2008, 2009 and 2010. On 1 October 2011, Bilger was elected district chairman of the CDU North Württemberg, the largest of the four CDU districts in Baden-Württemberg. He won clearly against his competitor, the former Secretary of State for Arts, Dietrich Birk. After his election as CDU district chairman, he ran again as country chairman of the Junge Union and was replaced in this office on 12 November 2011 by the Mannheim CDU city councillor Nikolas Löbel.
In the 2009 federal election, Bilger won the direct mandate in constituency of Ludwigsburg with 39.9% of the vote and became a member of the German Bundestag. In the 17th Bundestag he was a full member in the Committee on Transport, Construction and Urban Development, a member of the Parliamentary Advisory Council on Sustainable Development and a deputy member of the Committees Health and Environment, Nature Conservation and Nuclear Safety. He was also a full member of the Enquete Commission Growth, Prosperity, Quality of Life. In the 2013 federal election, Bilger won 50.4% again the direct mandate in constituency of Ludwigsburg. In the 18th Bundestag, he was a full member in the Parliamentary Advisory Council on Sustainable Development, the Committee on Transport and Digital Infrastructure and in the Joint Committee. He has also been Chairman of the MIT Transport Forum since 2013 and since 2016 a full member of the Conciliation Committee of the German Bundestag and the Bundesrat. On the Committee on Transport and Digital Infrastructure, Bilger served as his parliamentary group's rapporteur on electric vehicles and alternative fuel vehicles. In addition to his committee assignments, Bilger also headed the Parliamentary Advisory Board on Electromobility. Furthermore, he was also Chairman of the Young Group, the association of all Union members under the age of 35, until January 2018. In the 2017 federal election, Bilger won again the direct mandate in the constituency of Ludwigsburg with 38.3%. He became once again a full member of the Committee on Transport and Digital Infrastructure. In the associated working group of the CDU / CSU parliamentary group, he was elected at the end of January 2018 with 95.5% of the votes as chairman and deputy chairman of the group. During the coalition negotiations between the Union and the SPD, Bilger was part of the working group on transport and infrastructure, led by Thomas Strobl, Alexander Dobrindt and Sören Bartol. Since 14 March 2018, he has been Parliamentary State Secretary at the Federal Ministry of Transport and Digital Infrastructure under minister Andreas Scheuer. In April 2018, he also became Federal Government Coordinator for Freight and Logistics.