The moose in "The Moose" represents life, nature, and the will to continue. The passengers on the bus are older and their minds are fixated on death and sickness; they all have friends and family who have died and are talking incessantly of their hardships.
...deaths, deaths and sicknesses;
the year he remarried;
the year (something) happened.
She died in childbirth.
That was the son lost
when the schooner foundered.
When the moose appears, they become fixated instead on its vitality and simple nature:
Some of the passengers
exclaim in whispers,
"Sure are big creatures."
"It's awful plain."
"Look! It's a she!"
(Quotes: Bishop, "The Moose," poets.org)
The moose is passing by and has no real interest in the bus, it sparks a feeling of something new in the passengers, instead of their tired, entropic accounts. They can see something alive and without deeper cares, and in the moose they can see themselves years back; they may see themselves today, if they take more time to enjoy their remaining lives. In its simplicity -- the moose is, after all, nothing more than a moose -- they see the joy of living without fear, rather than the pain of living inside regret.