Bauer was active in West German motor racing during the post-war period when the country's motorsport scene was rebuilding around events like the Mille Miglia and the Nürburgring endurance races. In April 1953, he co-drove a Porsche 356 Super 1500 alongside Hans Herrmann at the Mille Miglia, the legendary Italian road race. The pair completed the gruelling course and finished in 30th position overall.
Bauer's most celebrated result came in 1954 when he drove an undermatched Lotus to fourth place at the 1000 km Nürburgring. The performance stood out because the Lotus was not considered a competitive machine in such company, and the result gave the young British manufacturer one of its earliest successes in a major international sports car event. The finish helped establish Lotus's reputation as a constructor capable of punching above its weight in endurance racing.
Bauer's sole Formula One World Championship entry came at the 1953 German Grand Prix, held at the Nürburgring. He drove a privately entered Veritas, a German marque that had emerged after the war using BMW-derived engines and that appeared sporadically in early Formula One competition.
In a starting field of thirty-four drivers, Bauer qualified 33rd, placing him near the back of the grid and ahead of only fellow Veritas entrant Oswald Karch. When the race began, Bauer managed to complete the opening lap and reach the second lap — a distinction that placed him ahead of several better-funded entrants who retired almost immediately, including Hans Stuck and Ernst Loof. His own race ended on the second lap when his engine expired, but not before he had advanced to 28th position by overtaking the two retiring cars plus Rudolf Krause and Maurice Trintignant.
The result scored no championship points, but the appearance marked Bauer as part of the generation of privateer drivers who filled out the grid in Formula One's early years, often running uncompetitive machinery against factory teams.
Bauer died on 3 June 1958 at the Nürburgring, the same circuit where both his Formula One start and his celebrated Lotus result had taken place. During a sports car race, Bauer was driving a 2-litre Ferrari when he failed to realise he had passed the chequered flag at the end of the race. Not recognising that the race was over, he continued at racing speed on what was meant to be a slowing-down lap and crashed fatally. He was 45 years old.
Bauer represents the category of amateur and semi-professional drivers who populated European motor racing in the early 1950s. His fourth-place finish at the 1954 1000 km Nürburgring in a Lotus remains a footnote in that constructor's early history, a result that demonstrated even lightly funded entries could achieve significant placings in endurance competition when conditions favoured consistency over outright speed.