Striking bus drivers picketed outside the Department of Education's headquarters at Tweed Courthouse on Monday.

A union proposal to suspend the city’s two-week-old school bus strike temporarily got a swift rejection this week from city officials, who said the plan would block cost-cutting measures for over a year.

The bus drivers union, Amalgamated Transit Union Local 1181, called a press conference today to announce that the city had turned down its proposal for a two-to-three month “cooling off” period during which drivers would return to work and the city would not solicit bids for new transportation contracts.

The union called the strike because the city is not including seniority protections for current drivers in the new contracts’ terms.

In a mediation session organized but not attended by the city, union president Michael Cordiello met on Monday with Justice Milton Mollen, who brokered an agreement to end the last bus strike, in 1979, and representatives from several major bus companies.

Cordiello said today that during mediation, he agreed to send drivers and matrons back to work for two to three months if the city would suspend the special education transportation bidding process and negotiate with the union.

But freezing bidding for two months would make it impossible to have new contracts signed by September, delaying new contracts for another school year, according to City Hall spokeswoman Lauren Passalacqua. “Postponing the bids would guarantee that the same billion-dollar contracts we have now stay in place next year,” she said.

City officials appear prepare to wait out the strike, which could last through the end of the school year. The Department of Education has revised its strategies for helping families use alternate transportation, and some school bus companies have trained replacement drivers and matrons. The department has certified 49 new drivers and 200 escorts since the strike started, officials said this week.

“We have shifted from broad initial preparations to more tailored options for students disproportionately affected by the absence of bus service,” Chancellor Dennis Walcott wrote in a message to principals sent late Tuesday. The city has assigned Walcott police protection at work and at home because of the strike.

On Tuesday, attendance in District 75 schools, which serve severely disabled students who rely heavily on yellow bus service, was at its highest level since the strike began. About 73 percent of students in those schools were present, compared to less than 65 percent all of last week.