The puppy, which has been named Gus by staff at the animal centre where he is being cared for, was discovered under a seat this week.
"
It must have been very frightening for such a young puppy to be on his own in unfamiliar and noisy surroundings
"
Steve Byrne, RSPCA
A passenger on the bus, which was travelling to Port Talbot, took Gus - a cross between a collie and a spaniel - to a local branch of the RSPCA.
Staff at the Llys Nini centre in Penllergaer, Swansea, where he is now being cared for, said he needed food and water when he came in, but his health is improving.
"He is doing remarkably well considering his ordeal - he is settling in well and is extremely friendly," said centre manager Steve Byrne.
"It must have been very frightening for such a young puppy to be on his own in unfamiliar and noisy surroundings," he added.
Seasonal message
Mr Byrne said Gus could have been an unwanted Christmas present.
"The RSPCA has to deal with many cases of abandonment all year round and we actively discourage people from buying pets as Christmas presents," he said.
"Often the new owners have tired of them after the festive season and abandon them without a thought.
"This incident looks like our seasonal message is still not getting through," he added.