Out of curiosity, I looked for a logo. FWIW I found this picture of an A. Borne bike somewhere in a quick search. It looks hand painted (?) Maybe there was more than one?
Zoomed in there is enough detail for a skilled graphic designer to trace it in Illustrator and 'unwrap' it from the tube well enough to make a repro decal, IMO.
I bet a pro sign painter could copy that too.