THE BRONX - Yellow school bus drivers have hit the picket line for day two of a citywide strike.

Parents are again being forced to make alternate arrangements to get their children to class after scrambling through the first hectic day without their usual bus service.

More than 8,000 members of the Amalgamated Transit Union Local 1181 are protesting to have job security for veteran drivers guaranteed in new contracts. The demand follows the city's announcement that it will open bus contracts for competitive bidding for the first time in more than 30 years.

Mayor Michel Bloomberg addressed the strike, insisting that the city can't meet union demands because of a state Court of Appeals ruling that made the Employee Protection Provision they want illegal. He added that he wants competitive bids in an effort to keep costs down.

Union President Michael Cordiello also spoke publicly yesterday, giving no indication that a compromise was within reach and calling the court ruling inaccurate.

Not all students are affected by the strike, but the city has rolled out plans to help those who are. Eligible students have received temporary MetroCards, and reimbursements will be available for parents who drive their kids or who use a car service.

Students are also being allotted an additional two hours to get to school before being marked tardy. Parents can call if their children can't make it and the absence will not be included on their permanent record.

The city's last school bus strike was in 1979 and it lasted for 14 weeks.