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Could be with Braillard 4936 (T35C) and 695-L (CH) for:

- #46 IX° Internationales Klausenrennen, 6-7th August 1932, Louis Braillard 4th in class (T35B or T51)
- #38 I° Grand Prix de Marseille, 25th September 1932, Louis Braillard 7th (T35C/51 ?)
- Boulevard Michelet Hillclimb, Marseille, 2nd April 1933, Louis Braillard
- #25 La Turbie hill-climb, 6th April 1933, Louis Braillard
- Mont Faron Hillclimb, 7th May 1933, Louis Braillard 1st
- XII° Les Alpilles Hillclimb, 14th May 1933, Louis Braillard


Could be with Braillard (T51) and 695-L (CH) :

4936 (T35C/51)
4936 with 51136 engine
4936 with 51125
51137
51134

for :
- #18 V° Grand Prix de Tunisie, Carthage, 29th March 1933, Louis Braillard with 695-L (CH) 11th > Bugatti Trust says 51134
- Course du Kilometre, Marseille, 1933, Braillard
- #6 II° Grand Prix de Nîmes, 4th June 1933, Louis Braillard 5th
- #36 II° Grand Prix de la Marne, 2nd July 1933,Louis Braillard DNF with 695-L (CH)
- #20 IV° Grand Prix de Belgique, 9th July 1933, Edgard Markiewicz "Marko" DNF
- #18 I° Grand Prix d'Albi, 27th August 1933, Louis Braillard 1st 
- #51 Mont Ventoux Hillclimb, 3rd September 1933, Louis Braillard 5th 
- Monte Ceneri Hillclimb - 3000cc, 24th September 1933, Louis Gaillard
- #8 IV° Masarykuv Okruh, 17th September 1933, Edgard Markiewicz "Marko" DNF
- #20 or 26 ? X° Grand Prix de Picardie, Péronne, 27th May 1934, Louis Braillard 4th 
- #18 I° Grand Prix de Montreux, 3rd June 1934, Louis Braillard DNF 
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Also with 695-L (CH)
T35C (probably 4936), VIII° Internationales Klausenrennen - 2000cc, 10th August 1930 with J. Karrer
or
T35C/51 (4936), VIII° Internationales Klausenrennen - 2300cc, 10th August 1930 with Escher
T36 (4751) with Karrer (CH)

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I am surprised how serious you guys are taking information from secondary sources in the internet. Very often they are wrong, and in general they are inadequate.
As example Klausen 1932, Braillard started with 2.3 litre Bugatti in the sports car class, so far so good. T35B or T51? If you have the period documents you will see that the entry form shows "year built 1931", so we can exclude a T35B. But why not a T43? They had one. So the only solution are photos showing Braillard with the car. And these confirm indeed it was a T51.

The T35B for Tunis is wrong, photo confirms that it was a T51. Nearly all internet race statistics sites are originally based on Sheldon's "Black Books" (http://www.formulaoneregister.com), of which "Golden Era" is by far the best as mistakes had been corrected by and by, but not all of them. Paul Sheldon and his companions did a tremendous work with these books, especially as they had been researched and written before the internet era, but as they cover motorsport history from the dawn in 1900 until the recent years it is understandable that not much attention could be given to individual races, drivers or cars. Unfortunately too much assumptions and speculations had been included, especially when it comes to Bugattis. In those days never type designations had been used in motor racing, there was even no column for that on entry forms. A Bugatti 2.3 litre therefore could have been a 35T, 35B, or 51, and a 1.5 litre car everything from a Brescia to a 51A. And very often their guesses had been wrong....

I have unfortunately no period documents, so I must rely on the Internet ...

so a T51 sports car

T47 (47155) Internationales Klausenrennen - sports cars up to 3000cc, 10th August 1930 with Escher

That's okay as long as you realize how unreliable these sources are, and that you don't take them as proof.

Yes

Yes, on loan from the factory.

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IX° Internationales Klausenrennen, 6-7th August 1932 (Beyond by Darren Galpin)

Burggalller T51A (1500cc)

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IX° Internationales Klausenrennen, 6-7th August 1932 (only bugatti)

- Kategorie Tourenwagen 3000cc
T44 2948cm3 (unknown), A. Scheibler (CH) 1st
- Kategorie Sportwagen 2000cc
T35C GP 1988cm3 1926 (4882), Pierre Rey (F) 4th
- Kategorie Sportwagen 3000cc
T35B GP 2262cm3 (unknown), Charley Jellen (D) 2nd
T35B GP 2262cm3 (unknown), Josef Karrer (CH) 3rd
#46 T35C/51 GP 2262cm3 (probably 4936), Louis Braillard (CH) 4th
T35B GP 2262cm3 (unknown), C. J. Godeffroy (CH) 6th
T35B GP 2262cm3 (unknown), R. Bonnet (F) 7th
T51A GP (4842 modified 8C-1500), Ernst G. Burggaller DNF
- Kategorie Rennwagen 1500cc
T37A Sport 1450cm3 (unknown), Hans Simons (D), 1st
T37 Sport 1492cm3 (unknown), Joseph Zigrand (NL) 3rd
- Kategorie Rennwagen 2000cc
T35C GP 1988cm3 1931 (4941), Louis Trintignant (F), Lukas Hüni (CH) 1st
T35C GP 1988cm3 (unknown), Ralph (F) 2nd
T35A Course Imitation "Tecla" 1988cm3 (unknown), J. Strittmatter (CH) 3rd
#81 T35C GP 1988cm3 1929 (unknown), Emma Munz (CH) 5th
#82 T35C GP 1988cm3 1929 (4921) 2678-RB6 (F), Mlle. Hellé-Nice (F) 6th
- Kategorie Rennwagen 3000cc
#87 T51 GP 2262cm3 (51124), Hans Stuber (CH) 2nd
#91 T51 GP 2262cm3 (unknown), Earl Howe (UK) 3rd
T35B GP 2262cm3 1930 (4956), A. Muff (CH) 4th
T35B GP 2262cm3 (unknown), F. Benoit (F) 6th
T35B GP 2262cm3 (unknown), Marcel Lehoux (F) 7th
T35B GP 2262cm3 (4948), Paul Pietsch (D) 9th
- Kategorie Rennwagen sup. 3000cc
#99 T53 GP 4900cm3 (53003) 8264-NV1 (F), Louis Chiron (F) 1st
#98 T53 GP 4900cm3 (53001) 8265-NV1 (F), Achille Varzi (I) 2nd

non identified
#41 T37 Sport (unknown) 379-C

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