A note for modern readers. A newspaper's society column in the horse
and buggy age might mention that some notables "arrived in a private coach"
to indicate that they traveled in style. The reference here to a private ass
(donkey) and cart is making fun either of the society pages or of the Miss Bradys.
You decide which.
William Percy French (1854-1920) was an Irish actor and painter who also wrote
a lot of funny songs. This is one of them.
Another one is here.