A source tells NY1 that the striking school bus drivers' union, Amalgamated Transit Union Local 1181, pitched a compromise to City Hall that would have put drivers back to work, but the city said no.

A source says the union asked Mayor Michael Bloomberg to slow down the bidding process for new bus contracts so all sides could have time to negotiate.

The drivers would have gone back to work while those talks took place, but the source says the city wouldn't agree.

Some bus routes returned Tuesday, with drivers and attendants from a different union who crossed picket lines on Staten Island, but many parents told NY1 they had no idea the buses were coming, and some were practically empty.

The striking drivers want job protections in any new contract with the city.

NY1 has reached out to City Hall for a response as of 11:30 p.m. Tuesday.

Out of the city's 7,700 routes, 12.5 percent are currently running for general education students, and about 37 percent for special education students.

The city says to check for updated route information online at schools.nyc.gov.