MIAMI — Appearing at an elementary school yesterday, Mayor Bloomberg and Governor Bush of Florida vowed to lobby Congress for four key education reforms.

Since writing an opinion piece for the Washington Post in August, the Republican pair have forged a political partnership in an attempt to boost their case for making changes to the federal No Child Left Behind Act, which is up for reauthorization next year.

The two toured a Miramar Elementary School, a Title 1 school located about 35 minutes outside Miami, and sat in on a vocabulary lesson in a fourth-grade class. As reporters and government staffers huddled around, they fit themselves into children’s chairs and desks and read sentences from a projector in the front of the room.

After a news conference with Mr. Bush in the library of the school, Mr. Bloomberg jetted to Little Havana for a Cuban lunch with Miami’s mayor, Manuel Diaz, at Versailles Restaurant, a gathering spot for the city’s Cuban powerbrokers.

The lunch —Mr. Bloomberg ordered a Cuban sandwich — was not the mayor’s only stop outside the school. Mr. Bloomberg, who owns a home in Palm Beach County equipped with horse stables for his daughter, also used the trip to address several other New York City agenda items.

Before appearing at the school, he spoke at a private meeting with union leaders from Change to Win, the group that recently splintered off from the AFL-CIO. The commissioner of the mayor’s Community Assistant Unit, Patrick Brennan, a former union operative who helped the mayor lock up labor support for his reelection last year, said the meeting, held at the Sheraton in Bel Harbour, included about 16 or 17 international and national union leaders and hit on a range of subjects including the mayor’s poverty commission and his gun control initiatives. The union includes seven powerhouse labor organizations, including the International Brotherhood of Teamsters, UNITE HERE, and the Service Employees International Union, whose affiliate in New York is Local 1199, the health care union run by Dennis Rivera.

The executive director of Change to Win, Greg Tarpinian, said the 2008 election “did not come up at all either from him or from us.”

He said the leadership of the labor group invited Mr. Bloomberg to yesterday’s monthly meeting some time ago as part of its effort to meet with political leaders nationwide. The group has already met with Governor-elect Spitzer as well as with the governors of Kansas and Michigan, he said.

Mr. Tarpinian called the mayor “one of the most important political leaders in the country” and said the group felt it was important to meet with him to discuss things such as reducing the income gap. While he stressed that 2008 was not mentioned, he said that if Mr. Bloomberg was a candidate he would be “attractive” and that “we would take him seriously.”

On the education front, Mr. Bloomberg, who also had the city’s schools chancellor, Joel Klein, with him on the trip, has said that New York will adopt some of the policies that Mr. Bush has pushed in Florida, including grading schools on an A through F scale. That effort is scheduled to go into effect citywide next year. He has also said that he wants to link teacher pay to performance, but the teachers union is opposed and has blocked that idea from contract negotiations.

Mr. Bloomberg said that while the performance gap between African American and Hispanic students and their white counterparts is narrowing, it is still “unconscionably high.”

With Mr. Bush’s term about to expire, his partnership with Mr. Bloomberg and their pledge to lobby Congress together could keep him in the public eye for a little longer. They both said the issue of education reform was not a partisan one.