According to the book "Dino: The Little Ferrari" by our Doug Nye, the Scuderia Ferrari had a motorcycle team from 1932-1934 which operated at top level with Bianchi and Rudge machines, for riders such as Giordano Aldrighetti, Carlo Baschieri, Giuseppe Fagnani, Aldo Pigorini, Francesco Lama, Guglielmo Sandri and a young Piero Taruffi.
Don't know how competitive the team was.
I know very well the great Nando Aldrighetti and the engineer Taruffi, Pigorini and Sandri who became a Moto Guzzi works rider, and also Lama winner of the Italian Motorcycle Championship in late 30s.
I know nothing about Carlo Baschieri and Giuseppe Fagnani.
In the book "Albo della Gloria" by Emanuele Carli, the famous book about racing fatalities, is listed a certain "Fagnani - Italy - 1933". Presumably he is Giuseppe Fagnani the same person, but I have nothing about his fatal crash.

According to Doug Nye Ferraris MC team from 1932-34 made around 91 starts in 39 events, won 43 times , added 12 secondplaces and five thirds, but didnt make enough money to stay in business.

On Ferraris transporters in those days varying sponsors , also for the MC team found their way. Ferrari also had a Rudge dealership , and possibly Norton (?) .

In the thirties the Scuderia Ferrari edited a magazine for few years. These have been repinted about 15 years ago. "If I am not mistaken, which I possibly am..." they contain also info on the bike team. Now I suppose their results have not been so glorious as in many Ferrari books there is only little mention about them.

I believe I have inquired on this forum before, but no one seems to have knowledge of any motorcycle extant today claiming a SF history.

Yes they most certainly did have a M/C team 32 thru 34 . Here's a link to the story . Hope you speak Italian though .

http://www.modelfoxbrianza.it/MotoScuderia.htm

An Appendix at the back of 'The Scuderia Ferrari' Orsini/Zagari (English text by D Nye) lists at least the main races or victories from 1932 to 1934 using Rudge and Norton motorcycles. I can't quite believe it is a comprehensive list despite it being fairly long as they seemed to either come in the top four or retired. But then the races Ferrari entered whether cars or bikes were more based on what they could win for prize money in those days, rather than entering championships etc. So I suppose they entered the winnable ones.

Ferrari started the motor bike team as a second activity in the Scuderia for finding and developping young italian talents.

1932 Drivers: Aldrighetti, Fieschi, Severi, Sandri and Ghersi on Rudge, Taruffi on Norton and Baschieri on 175 cc Benelli; Sandri made the SF debut with a win at the Gran Premio Primavera (Spring GP) at the Circuito di Modena.

1933 Drivers: Aldrighetti, Fagnani and Pigorini on Rudge;

1934 Drivers: Aldrighetti, Colabattisti and Pigorini on Rudge.

Team manager was Renzo Saracco Ferrari (nephew of EF), chief mechanic Arturo Pennacchio.

Why English bikes? Italian motor bikes were scarce and the English brands were simpy superior in racing at the time. Rudge was a brand Ferrari already had contacts with as they supplied the Alfa racers with wire wheels from Rudge Whitworth (made in licence by Carlo Borrani (and Ambrosetti) from 1922 on).

Aldrighetti was the most succesful rider: winning seven races in 1932, nine in 1933 as well as that years italian title for the 500 cc class, and three in 1934.

1934 was the least succesful season and may have been a reason next to costs to close down the motocycle team.

There is a nice piece on this at : www.motorvalley.it

Giuseppe Fagnani joined the Scuderia Ferrari in 1932, having his debut in the Circuito Pietro Bordino at Alessandria, on a Rudge 250. He won the Varese-Campo dei Fiori hillclimb in 1932 and the Circuito di Modena in 1933. His last result of the season was reported as the 3rd place in the Circuito di Rimini, held on 06 August 1933. Fagnani lost his life in an accident which happened during the Circuito di Luino, held on 17 September 1933, riding a Rudge.
(Book "Il Mistero delle Moto Inglesi di Ferrari"" by Nunzia Manicardi, Edizioni Il Fiorino, Modena, August 2009, ISBN 978-88-7549-291-5, page 80).

I believe the team had dealings with Graham Walker, who was some sort of distributor for Rudge at the time.