School district officials have developed two variations of a proposed new bus schedule in an effort to allay parents’ concerns over the cost-saving plan.

Under the first variation, Elephant’s Fork, Booker T. Washington, Oakland, Creekside, Nansemond Parkway and Southwestern elementary schools would start one hour and 35 minutes earlier than presently, and Driver, Florence Bowser, Mack Benn Jr., Kilby Shores, Northern Shores and Hillpoint would start one hour earlier than they do now.

High schools and middle schools would start 50 minutes and an hour and a half later, respectively, and the variation would save the same annual amount — currently estimated at $680,000 — as the original proposal, district Assistant Superintendent for Instructional Services Kevin Alston told Thursday’s School Board meeting.

District Superintendent Deran Whitney declared his support for the second variation, which Alston reported would save $280,000 less. “The cost saving isn’t as much as we would like … but this would be my recommendation,” Whitney said.

Under the second variation, Elephant’s Fork, Kilby Shores, Northern Shores, Booker T. Washington and Southwestern would start a half-hour earlier, and the other elementary schools 15 minutes later. Middle schools would start 15 minutes earlier and high schools 50 minutes later.

Parents at the meeting appeared to greet the tweaks with some measure of satisfaction, after three public input sessions about three weeks ago on the original proposal yielded various questions and concerns, mostly regarding child care and impacts on work and family schedules.

While all secondary schools now start at 7:40 a.m. and elementary schools at 9 a.m., the proposal put forward Jan. 12 called for dividing elementary schools between “A” and “B” bell times — though distributed differently than both variations presented Thursday — and starting middle schools 15 minutes earlier and high schools 50 minutes later.

“There is no way we are going to be able to please everyone,” Alston said. “Our intentions were honorable. I can assure you of that.”

Savings from the original schedule proposal — equal to the first variation but less in the case of the second — are factored into the district’s proposed 2013-2014 budget, which asks the city for an extra $9 million to provide raises and improvements.

Inviting more feedback from citizens before a March 21 meeting to approve the final version of the budget to send to the city, the district will post online details of the three proposed schedules, along with pro and cons.

As he has before, Whitney told the School Board meeting that the level of education public school students currently receive in Suffolk will likely take a hit if the city is not forthcoming with extra funds.

Employee compensation and benefits account for 84 percent of the budget, he said, adding, “When we talk about reducing the budget significantly, we have to talk about reducing people.”

The proposed schedules and be viewed and commented on at www.spsk12.net.