The transportation authority introduced an ad campaign in December warning pedestrians about walking and texting near buses and, according to a spokesman, Kevin Ortiz, the agency plans to outfit some buses with an audio warning system this fall.

In 2014, at least nine pedestrians were killed when transportation authority buses struck them, usually while the buses were turning. Transit groups keep a tally of the lives lost, among them Marisol Martinez, a 21-year-old nursing student from Brooklyn, and Julian Porres, an 88-year-old from the Bronx who died nearly a month after he was struck.

Their deaths were among 132 pedestrian traffic fatalities in the city last year. City officials said the figure was the lowest on record, but warned that more measures were needed to bring the number to zero.

In December, another transportation authority bus driver, Reginald Prescott, was arrested when his bus struck a 78-year-old man in East Flatbush, Brooklyn. Amalgamated Transit Union Local 1056 said one of its members had been charged under the law for an accident in November in Queens, but declined to give the driver’s name.

A day before Mr. DeJesus’s arrest, several City Council members introduced a bill to amend the law so that it would not apply to bus drivers. A sponsor of the bill, I. Daneek Miller, a former bus driver, said the law was never intended to be used against bus drivers. A provision in original bill says it does not apply to drivers working for the city, state or federal government who are “actively engaged” in work that requires a vehicle at a location interfering with a pedestrian’s right of way. Mr. Miller said that should include bus operators.

Bus operators involved in a fatality or serious injury cannot drive while it is being investigated, Mr. Miller said, and would face a disciplinary process. “Short of someone being on the cellphone, texting, driving on the wrong side of the street, short of drugs or alcohol — I don’t see a criminal offense here,” he said.

The ad campaign, which showed a woman texting when a bus struck her, led to outrage among transit groups because, they said, it appeared to blame the victim.