The month-long school bus strike that affected more than 100,000 public school children is over, and by the middle of this week, buses will be ready to take kids to school.

Schools Chancellor Dennis Walcott on Monday thanked parents and students for their patience, and said to expect a few hiccups as service resumes Wednesday morning.

“Just as with the first day of school, and also the first day after Hurricane Sandy, there may be some disruptions and we should treat this like a first day of school, especially since this is an unusual week,” Walcott said.

Mid-winter break was shortened to just two days this year – Monday and Tuesday – from the usual five, to make up days lost by Sandy which shut down schools for a full week.

Walcott added that after plummeting to just 49 percent at the strike’s beginning, attendance among special needs kids rose to 78 percent by last week.

The cost of getting those kids to school by alternative means appears – for now – to have been significantly less than the cost of busing them under ordinary circumstances.

Walcott said the cost of reimbursing families stands at roughly $20.6 million, including $17 million for MetroCards, and about $3 million to reimburse parents for fuel (if they drove their own vehicle), or fares (if they used a car service).

Payments to bus companies dropped by $80 million during the strike.

Parents have one month remaining to submit their receipts, so the cost of reimbursements could rise considerably.

Walcott emphasized that the decision of the Local 1181 union bus workers to end their strike would bring bigger changes to the busing system. The new request fro bids on some of the city’s school bus routes has already brought in 32 new vendors, Walcott said.

“We opened up a process that had been closed for 33 years. So you had bus contracts that were extended year after year after year after year,” Walcott said. “And now what we’ve been able to do is open up the process, shed some sunlight on it, and have people respond based on 21st century buses that are out there.”

Walcott said the city could save roughly $100 million as a result of a more competitive bidding process. But he conceded there were other areas to find cost savings beyond the bus contracts.

He said that the Department of Education will review existing maps for inefficiency.

And the city is exploring the possibility of deploying smaller vehicles for routes that are traveled only by a few students attending highly specialized schools.