In Eberron is it feasible in the world to have a one or two man airship or earth sled such as a “sky bike” or “earth bike”? It's certainly FEASIBLE – the Sulatar drow of Xen'drik use 2-person flying fire-sleds.
— Keith Baker (@HellcowKeith) September 19, 2017
The catch is that in Eberron magic is a science. At the current stage of development it takes a dragonmarks to control elemental vehicles.
— Keith Baker (@HellcowKeith) September 19, 2017
If you choose to advance elemental science to a point where you don't need a dragonmark you could, but that would impact Orien & Lyrandar.
— Keith Baker (@HellcowKeith) September 19, 2017
Fun fact – single person airships exist in real life, and actually predate airplanes.
I highly recommend that anyone interested in such craft should look up Alberto Santos-Dumont, the largely-forgotten gentleman-pioneer of early flight.