She rang the doorbell of a home, prepared to provide an unusually personal reminder to a boy’s family about his bus route this fall. What she got instead were complaints about how the bus routinely ran late last year by as much as a half hour.

“Unfortunately, we did have lots of problems last year with routing,” Johnson said. “But we’re hoping we made the right changes.”

Johnson does not usually take time out of her hectic schedule to partake in the annual dry run of more than 3,600 bus routes, which began last week, but she is determined to make sure that the chronically late buses that have defined the opening of the past two school years are history.

Over the last several months, Johnson has enacted a number of changes, most notably naming a new transportation director, drawing up routes earlier, and cross-referencing computer-generated travel times with drivers’ knowledge of the streets and problematic intersections.

The true test will come this week with the start of the school year, when the School Department will begin transporting more than 33,000 students to 228 public and private schools that start at different times and draw students from a mix of neighborhoods. While some initial confusion is unavoidable, as late-registering students join the system, much is riding on the School Department’s ability to have things running smoothly well before month’s end.

“It’s just so incredibly important for this year to be different,” said Mary Tamer, a School Committee member who was one of the most outspoken critics of Johnson’s handling of the transportation crisis. “One of my biggest concerns was not only were students missing critical instructional time, thousands were also missing free or reduced-priced breakfasts. It’s very difficult for students with empty bellies to learn.”

There is also a lot on the line for Johnson herself, who is trying to regain her footing after revelations this summer about her support of a headmaster who admitted to sufficient facts after being charged with assaulting his wife.

Johnson is facing calls for her ouster from more than 200 parents, teachers, and at least one city councilor, who are upset that she wrote a letter of support for Rodney Peterson to a judge last summer and carried through with promoting him to co-headmaster of the O’Bryant School of Mathematics and Science.

She, however, still has strong support from Mayor Thomas M. Menino and several other city leaders, including the School Committee’s chairman, the Rev. Gregory Groover.

Chronically late buses have been among the biggest blemishes on Johnson’s five-year record of leading the Boston schools. An astonishing 37 percent of all buses ran as much as an hour late at the start of the last school year and she failed to quickly remedy the problem, prompting a few School Committee members at the end of October to declare a crisis as one out of four buses still ran late.

Even Menino intervened out of frustration, assigning one of his top aides to help fix a school transportation system he deemed to be “broken.”

Eventually, the School Department pushed up its on-time arrival performance to higher than 90 percent on most days in the last half of the school year, but it was no easy task.

The School Department operates a mammoth transportation system at a cost of more than $80 million, shuttling students across the city on more than 700 buses. With most buses running three separate trips in the morning and three more in the afternoon, a mistimed route can domino into later runs, creating one late stop after another and an onslaught of angry complaints from students, parents, principals, and teachers.

That is a scenario that repeatedly played out during the previous two school years. In 2010-11, the School Department and the drivers largely blamed the tardiness on a new computerized routing system that often grossly undercalculated the time for buses to travel routes in Boston’s often traffic-clogged streets and sometimes put buses on streets too narrow to navigate.