The important bit of this sentence is not “dash about”, but “motor-cars”. The point being that
the character ‘Old Popper’ had introduced his tale with the claim that
“The thing actually happened to me—years ago, many years ago. … It happened when I was quite a youngster, and was working as a clerk in a solicitor’s office.”
When would this have been? ...
"Dash" can mean a lot of things, but I think here connotes mostly "movement", as if the question was "did commercial travelers go from place to place in motorcars?", with an added side-connotation of doing so stylishly.
I asked Google books for "dash about town" and came up with instances like this recent one (from
Juliet Clutton-Brock's 1992 Horse)
This sounds very like ‘The Seventh Voyage of Ijon Tichy’ by Stanisław Lem, collected in The Star Diaries. The collection was first published in Polish as Dzienniki Gwiazdowe in 1957; the English translation by Michael Kandel appeared in 1976. This story has all the features you remembered:
Ijon Tichy is travelling alone in a spaceship:
It was on a Monday,...