Sgt Louise Lucas, 41, a mother-of-three, was killed and her eight-year-old daughter suffered minor injuries in Tuesday's collision on The Kingsway.
It was the second death in 18 months.
Swansea council is to install barriers on the road's central reservation and is now changing the traffic flow in the bus lane "as quickly" as possible.
The current system has two lanes of normal traffic travelling west on one side of the road, with two lanes of public transport - one going east and one west - on the other side.
In September 2013, Daniel Foss, 37, from Reynoldston, Gower, died after being struck by a National Express bus on the road and there have been other incidents since the system was introduced in 2006.
Nearly 3,000 people have signed a petition calling for changes, including a return to a traditional two-way system on the road.
Swansea Council leader, Rob Stewart, said the council was "deeply saddened" by Sgt Lucas's death and acknowledged the public had "raised concerns" about The Kingsway.
He said the authority had been working for "some time" to improve the road layout in the city centre.
"We are bringing forward some of the potential measures and we're working in partnership with others, including local bus operators, to address concerns as quickly as possible," he said.
"These measures are the ones we can do immediately, but others will follow as we develop our plans."
The changes will affect all bus and coach operators, taxis and private hire firms but would take "some time" because legal steps had to be taken and buses needed re-routing.
The council announced the move after talks with Justin Davies, managing director of local bus operator, First Cymru, and the chair of the Confederation of Passenger Transport Wales.
Traffic will be stopped from travelling eastbound on a Swansea city centre road where an off-duty police officer died after being hit by a bus.