In 1962 the right-handed Bungert reached the quarterfinals of the International Australian Championships, the doubles finals of the International French Championships and the International Tennis Tournament of Monte Carlo.
Bungert was ranked as high as World No. 4 for 1964 by Lance Tingay of The Daily Telegraph.
After reaching the semifinals in 1963 (beating Roy Emerson before losing to Chuck McKinley) and 1964 (losing to Emerson), the unseeded Bungert was the second German player (thirty years after Gottfried von Cramm) to reach the Wimbledon men’s finals in 1967 when he beat Roger Taylor in five sets.
However, he lost the final in straight sets against the Australian John Newcombe.
In 1970 he (with Christian Kuhnke) was part of the German Davis Cup team which lost the finals against the U.S. 0:5. In July of the same year he won his only career singles title in Düsseldorf.
In the eighties Bungert was captain of the German Davis Cup team (Boris Becker and Michael Westphal) which lost the finals against Sweden 2:3. Nikola Pilić became his successor as captain.
Round 2
Wilhelm Bungert 1 *
Andras Szikszai
6-6
6-2
6-2
Round 3
Wilhelm Bungert 1 *
Daniel Pierre Moreau
6-1
6-0
Quarterfinals
Wilhelm Bungert 1 *
Stefan Koudelka
6-4
6-4
6-3
Semifinals
Wilhelm Bungert 1 *
Barry Phillips-Moore
14-12
4-6
8-6
6-1
Final
Christian Kuhnke 1 *
Wilhelm Bungert
6-1
6-8
6-2
6-2
Round 1
Wilhelm Bungert 1 *
Patrick Proisy
2-6
6-0
6-3
Round 2
Wilhelm Bungert 1 *
Georges Goven
2-6
6-3
7-5
Quarterfinals
Wilhelm Bungert 1 *
Nick Kalogeropoulos
6-3
2-6
6-1
6-1
Semifinals
Wilhelm Bungert 1 *
Željko Franulović
3-6
1-6
7-5
6-1
6-2
Final
Istvan Gulyas 1 *
Wilhelm Bungert
6-1
6-3
3-6
7-5
Round 2
Wilhelm Bungert 1 *
Bryan Burrell
6-3
6-1
Round 3
Wilhelm Bungert 1 *
Onny Parun
6-3
3-6
4-6
6-3
6-1
Quarterfinals
Wilhelm Bungert 1 *
Bobby Wilson
6-4
3-6
6-1
6-2
Semifinals
Wilhelm Bungert 1 *
Jan Erik Lundquist
8-10
8-6
6-4
6-1
Final
Martin Mulligan 1 *
Wilhelm Bungert
6-2
6-2
6-3
Round 1
Wilhelm Bungert 1 *
Ewie Cronje
6-3
7-5
Round 2
Wilhelm Bungert 1 *
Frank D. McDonald
6-3
6-4
Round 3
Wilhelm Bungert 1 *
Hans Jurgen Pohmann
6-3
6-4
Quarterfinals
Wilhelm Bungert 1 *
Torben Ulrich
10-8
6-0
Semifinals
Tom Okker 1 *
Wilhelm Bungert
9-7
6-4
Round 1
Wilhelm Bungert 1 *
Ray J. Wilson
8-6
8-6
7-5
Round 2
Wilhelm Bungert 1 *
Frank Froehling III
10-8
6-3
1-6
6-3
7-5
Round 3
Wilhelm Bungert 1 *
Abe Segal
6-2
3-6
6-2
6-3
Round 4
Wilhelm Bungert 1 *
Bobby Wilson
1-6
5-7
6-1
7-5
9-7
Quarterfinals
Wilhelm Bungert 1 *
Thomaz Koch
6-4
4-6
4-6
6-1
6-3
Semifinals
Wilhelm Bungert 1 *
Roger Taylor
6-4
6-8
2-6
6-4
6-4
Final
John Newcombe 1 *
Wilhelm Bungert
6-3
6-1
6-1
Round 2
Wilhelm Bungert 1 *
Howard Broun
7-5
6-2
Round 3
Wilhelm Bungert 1 *
Gunther Bosch
6-2
6-2
Quarterfinals
Wilhelm Bungert 1 *
Graham Stilwell
3-6
6-2
6-3
Semifinals
Wilhelm Bungert 1 *
Koji Watanabe
6-3
3-6
6-3
6-4
Final
Martin Mulligan 1 *
Wilhelm Bungert
8-6
6-2
2-6
6-4
Round 2
Wilhelm Bungert 1 *
Daniel Pierre Moreau
?
Round 3
Wilhelm Bungert 1 *
Nick Kalogeropoulos
6-4
6-4
Quarterfinals
Wilhelm Bungert 1 *
Detlev Herdy
7-5
4-6
6-2
Semifinals
Wilhelm Bungert 1 *
Colin Stubs
7-5
6-4
9-7
Final
Martin Mulligan 1 *
Wilhelm Bungert
6-4
3-6
6-4
6-4
Round 2
Wilhelm Bungert 1 *
Al G. Hill Jr.
6-1
6-2
Round 3
Wilhelm Bungert 1 *
Clay Iles
4-6
6-4
6-2
Quarterfinals
Wilhelm Bungert 1 *
François Jauffret
8-6
6-3
Semifinals
Wilhelm Bungert 1 *
Bob Hewitt
3-6
6-4
6-4
Final
Istvan Gulyas 1 *
Wilhelm Bungert
6-4
4-6
8-6
9-7
Round 1
Wilhelm Bungert 1 *
Bob Trapenberg
6-1
6-1
Round 2
Wilhelm Bungert 1 *
Frank Arendt
6-0
6-4
Round 3
Wilhelm Bungert 1 *
Peter Pokorny
9-7
6-3
Quarterfinals
Wilhelm Bungert 1 *
Istvan Gulyas
6-3
7-5
Semifinals
Wilhelm Bungert 1 *
Boro Jovanovic
3-6
6-4
6-1
Final
Wilhelm Bungert 1 *
Martin Mulligan
1-6
6-3
6-4
4-6
6-4
Round 1
Wilhelm Bungert 1 *
Francis Rawstorne
3-6
6-0
6-3
Round 2
Wilhelm Bungert 1 *
Andrew J. Pattison
6-3
6-4
Round 3
Wilhelm Bungert 1 *
Anthony (Tony) Wolpert
9-7
6-3
Quarterfinals
Wilhelm Bungert 1 *
Jackie Saul
6-3
6-3
Semifinals
Wilhelm Bungert 1 *
Martin Mulligan
6-3
6-3
Final
Wilhelm Bungert 1 *
Ray Moore
10-8
6-3
6-2
Round 2
Wilhelm Bungert 1 *
Jean Bergmann
6-4
6-1
Round 3
Wilhelm Bungert 1 *
Ernst Blanke jr
2-6
6-3
6-2
Quarterfinals
Wilhelm Bungert 1 *
Michael Sangster
0-6
6-3
6-4
Semifinals
Wilhelm Bungert 1 *
Bob Hewitt
6-4
6-1
Final
Wilhelm Bungert 1 *
Ion Tiriac
5-7
8-6
6-4
Round 1
Wilhelm Bungert 1 *
Heinrich Bertschinger
?
Round 2
Wilhelm Bungert 1 *
Mr. Gemocek
?
Round 3
Wilhelm Bungert 1 *
Paul Pavich
5-7
6-2
6-1
Quarterfinals
Wilhelm Bungert 1 *
Billy Knight
1-6
8-6
6-2
6-2
Semifinals
Wilhelm Bungert 1 *
Wolfgang Stuck
10-8
0-6
6-3
6-3
Final
Wilhelm Bungert 1 *
Bob Hewitt
5-7
5-7
6-4
6-3
6-3
Round 1
Wilhelm Bungert 1 *
Günther Sanders
6-4
3-6
6-4
5-7
6-1
Round 2
Wilhelm Bungert 1 *
Klaus Peschanel
6-0
3-6
6-4
8-6
Quarterfinals
Wilhelm Bungert 1 *
Uwe Gottschalk
6-4
6-2
6-2
Semifinals
Wilhelm Bungert 1 *
Adolf Kreinberg
6-4
6-2
6-2
Final
Wilhelm Bungert 1 *
Dieter Ecklebe
6-4
6-4
3-6
6-3
Round 1
Wilhelm Bungert 1 *
Ray Moore
8-6
7-5
1-6
3-6
6-2
Round 2
Wilhelm Bungert 1 *
Keith Diepraam
5-7
6-3
3-6
8-6
6-2
Round 3
Wilhelm Bungert 1 *
Michael Sangster
6-4
4-6
6-3
6-3
Round 4
Wilhelm Bungert 1 *
Jorgen Ulrich
3-6
6-2
6-3
6-4
Quarterfinals
Wilhelm Bungert 1 *
Rafael Osuna
6-4
6-2
6-3
Semifinals
Roy Emerson 1 *
Wilhelm Bungert
6-3
15-13
6-0
Round 2
Wilhelm Bungert 1 *
Dimitri (Tim) Sturdza
5-7
6-4
7-9
7-5
6-4
Round 3
Wilhelm Bungert 1 *
Donald Dell
6-3
9-7
6-3
Quarterfinals
Wilhelm Bungert 1 *
Boro Jovanovic
3-6
6-4
6-4
6-4
Semifinals
Wilhelm Bungert 1 *
Manuel Santana
6-3
8-6
4-6
6-1
Final
Wilhelm Bungert 1 *
Christian Kuhnke
0-6
6-4
7-5
6-2
Round 1
Wilhelm Bungert 1 *
Michael Sangster
6-3
7-5
6-3
Round 2
Wilhelm Bungert 1 *
Eric Drossart
10-8
6-8
6-3
6-3
Round 3
Wilhelm Bungert 1 *
Toomas Lejus
6-4
3-6
6-3
6-4
Round 4
Wilhelm Bungert 1 *
Jose-Luis (Lis) Arilla Lopez
4-6
6-3
6-0
10-12
7-5
Quarterfinals
Wilhelm Bungert 1 *
Roy Emerson
8-6
3-6
6-3
4-6
6-3
Semifinals
Chuck McKinley 1 *
Wilhelm Bungert
6-2
6-4
8-6
Round 1
Wilhelm Bungert 1 *
I. Ezzat
6-3
6-8
6-3
Round 2
Wilhelm Bungert 1 *
Kamel Moubarek
1-6
6-3
6-2
Round 3
Wilhelm Bungert 1 *
Jozef Orlikowski
0-6
6-3
6-3
Quarterfinals
Wilhelm Bungert 1 *
Jose-Luis (Lis) Arilla Lopez
3-6
11-9
7-5
Semifinals
Wilhelm Bungert 1 *
Wolfgang Stuck
5-7
6-2
11-9
6-1
Final
Jan Erik Lundquist 1 *
Wilhelm Bungert
6-2
6-2
6-2
Round 2
Wilhelm Bungert 1 *
Noel Harford
7-5
6-4
6-3
Round 3
Wilhelm Bungert 1 *
Jeff Sacks
6-0
7-5
6-1
Quarterfinals
Wilhelm Bungert 1 *
Clive Brebnor
6-4
6-4
6-3
Semifinals
Wilhelm Bungert 1 *
Cliff Drysdale
8-10
6-2
6-3
6-3
Final
Wilhelm Bungert 1 *
Gordon Forbes
6-4
6-4
8-6
Round 1
Wilhelm Bungert 1 *
Kenneth Frank (Ken) Weatherley
6-1
6-0
Round 2
Wilhelm Bungert 1 *
Francis Rawstorne
6-1
6-2
Round 3
Wilhelm Bungert 1 *
Carlos Alberto Fernandes
6-4
6-4
Quarterfinals
Wilhelm Bungert 1 *
Bob Hewitt
6-4
6-1
Semifinals
Chuck McKinley 1 *
Wilhelm Bungert
6-0
7-5
Round 1
Wilhelm Bungert 1 *
Christian Viron
3-6
6-1
6-1
Round 2
Wilhelm Bungert 1 *
Jean Noel Grinda
4-6
6-1
6-1
Quarterfinals
Wilhelm Bungert 1 *
Billy Knight
7-5
7-5
Semifinals
Wilhelm Bungert 1 *
Gérard Pilet
6-4
6-0
Final
Pierre Darmon 1 *
Wilhelm Bungert
6-1
6-0
0-6
6-2
Round 1
Wilhelm Bungert 1 *
Wolfram Schneiders
6-4
6-3
6-3
Round 2
Wilhelm Bungert 1 *
Uwe Gottschalk
6-4
6-2
6-4
Quarterfinals
Wilhelm Bungert 1 *
Peter Scholl
6-3
6-3
6-2
Semifinals
Wilhelm Bungert 1 *
Dieter Ecklebe
6-3
4-6
6-3
6-0
Final
Wilhelm Bungert 1 *
Wolfgang Stuck
7-5
6-0
6-1
Round 1
Wilhelm Bungert 1 *
Hans Joachim Plotz
6-1
6-0
6-1
Round 2
Wilhelm Bungert 1 *
Adolf Kreinberg
6-4
4-6
6-0
9-11
6-1
Quarterfinals
Wilhelm Bungert 1 *
Harald Elschenbroich
8-6
10-8
6-1
Semifinals
Wilhelm Bungert 1 *
Bodo Nitsche
6-2
?
8-6
Final
Ingo Buding 1 *
Wilhelm Bungert
9-7
6-4
2-6
8-6
Round 1
Wilhelm Bungert 1 *
Frank Arendt
?
Round 2
Wilhelm Bungert 1 *
Dieter Schultheiss
?
Quarterfinals
Wilhelm Bungert 1 *
Orlando Garrido
6-1
6-4
Semifinals
Wilhelm Bungert 1 *
Eric Drossart
6-4
6-0
Final
Wilhelm Bungert 1 *
Arthur Schroder
6-1
9-7
6-3
Round 1
Wilhelm Bungert 1 *
Mr. Hale
6-3
6-0
Round 2
Wilhelm Bungert 1 *
Gerhard Muller
6-2
6-2
Round 3
Wilhelm Bungert 1 *
Werner Mertins
6-4
7-5
Quarterfinals
Wilhelm Bungert 1 *
Ulf Schmidt
6-3
0-6
6-4
Semifinals
Dieter Ecklebe 1 *
Wilhelm Bungert
6-3
2-6
6-4
Round 1
Wilhelm Bungert 1 *
Arthur Schroder
6-2
6-4
6-1
Round 2
Wilhelm Bungert 1 *
Lothar Pawlik
6-3
6-3
9-7
Quarterfinals
Wilhelm Bungert 1 *
Franz Feldbausch
6-2
6-0
6-4
Semifinals
Wilhelm Bungert 1 *
Christian Kuhnke
6-2
4-6
6-4
7-5
Final
Wolfgang Stuck 1 *
Wilhelm Bungert
7-5
6-4
6-1