Remember that Bugatti, like Porsche and others, did a lot of engineering work for others. In Bugatti's case, that included a small car for Peugeot, a railcar for the French railroads (not sure which one), etc. And Bugatti especially solicited that work very actively - all the way to building a prototype railcar and presenting it to the railroad without a single order (I think, but obviously, this is outside my realm of expertise).
So it was in his interest to have a large portfolio of ideas - many of which never were executed. Some were, though, like those miniature cycling motors. However, I suspect the goal was to show to prospective clients what Bugatti could do - and a miniature engine is much easier to bring along to a meeting than a full-size Grand Prix car. (Also easier to make if one has skills, but only a small, albeit well-equipped shop such as Bugatti had after WW II.)
I doubt those engines were intended for marketing - even Herse and Singer "moteurs" used rather ordinary Mosquito (?) engines. One major problem with bikes is that the owners don't like to maintain them like you would have to do with a motor like that. (Not speaking of the cost - I doubt the little engine was much cheaper to make than a full-size Bugatti engine! Did it require special warm-up plugs, special fuel, etc.?)
However, about the Bugatti multi-tubed bicycle - despite being Francophile, I cannot get excited. M. Bugatti was not known as a cycling enthusiast (photos show him on horseback, if not on foot), so I doubt he had a good understanding of what was involved in designing a good bicycle. If he had been a "praticant" (like, for example, Rene Herse, who worked in aviation, but was a passionate and competitive "cyclotouriste"), I am sure he could have proposed some brilliant improvements.
Jan Heine, Seattle (who admires Bugatti cars, but feels that makers should stick to what they do best. No Rene Herse cars for me, either!)