Cardiff Bus workers who are members of the Unite union carried out two strikes last week after rejecting a 5% pay increase.
More than 500 members took strike action on September 2 and September 5 after talks between the union and the operator broke down. Members of the Unison union had previously accepted the same offer.
Cardiff Bus apologised to service users for the inconvenience and said it was trying to provide services to as many parts of the city as possible.
Further strikes are planned through September and October. 48-hours strikes are due to take place on September 19-20, October 1-2 and October 17-18, with a further 24 hour strike on October 11. Much of the action has been timed to coincide with the upcoming Rugby World Cup.