The bus was set alight after being pelted with petrol bombs at the junction of Lanark Way and Shankill Road in west Belfast, the PSNI said.
It was one of a number of incidents on Wednesday evening that took place on the peace line street that links the loyalist Shankill Road with the nationalist Springfield Road.
Writing on Twitter, Mr Johnson said: "I am deeply concerned by the scenes of violence in Northern Ireland, especially attacks on PSNI who are protecting the public and businesses, attacks on a bus driver and the assault of a journalist.
"The way to resolve differences is through dialogue, not violence or criminality."
The Northern Ireland Executive is to meet on Thursday morning to be briefed on the situation.
Leaders will meet for the briefing at 10am, an hour before the Stormont Assembly is to be recalled to discuss the recent scenes of violence.
News of the Executive meeting was confirmed late on Wednesday night with trouble still raging on the streets of Belfast.
Deputy First Minister Michelle O'Neill said: "The Executive will meet tomorrow morning to be briefed on the violence and street disorder which is causing huge distress in local communities at this time.
"Those involved in violence, criminal damage, manipulation of our young people and attacks on the police must stop."
It follows several nights of unrest in loyalist communities amid tensions over the Northern Ireland Protocol on Brexit and the PSNI's handling of alleged coronavirus regulation breaches by Sinn Fein at the funeral of republican Bobby Storey.
Stones were thrown at police while a press photographer was assaulted nearby during the course of their work on Wednesday evening.
Later on Wednesday night, the gates of the peace line on Lanark Way were opened, leading to clashes between loyalists and nationalists.
Social media footage captured petrol bombs being thrown from both sides of the wall.
First Minister Arlene Foster condemned the attacks on Twitter, saying: "There is no justification for violence. It is wrong and should stop."
She later added: "This is not protest. This is vandalism and attempted murder. These actions do not represent unionism or loyalism.
"They are an embarrassment to Northern Ireland and only serve to take the focus off the real law breakers in Sinn Fein. My thoughts are with the bus driver."
Deputy First Minister and Sinn Fein vice president Michelle O'Neill said: "Disgraceful scenes of criminality tonight including a potentially lethal attack on bus driver and assault on journalist.
"Unequivocal condemnation needed and protests should be called off immediately - police need support not politicking."
The Chief Constable of the PSNI Simon Byrne has pleaded for the ongoing unrest to stop.
He tweeted: "The ongoing street disorder must stop. I am open to dialogue with anyone who is willing to work with me to resolve the issues facing our community.
"My message to those engaged in violence tonight is go home before someone is seriously injured, violence is not the answer."
Arlene Foster, along with the other unionist parties, had called for the Chief Constable to resign over the Bobby Storey funeral debacle.
Minister for Infrastructure Nichola Mallon described the attack on the bus as "sickening".
She said: "Those attacking their own communities and their own public services are achieving nothing and if this doesn't stop now it is only a matter of time before someone is seriously injured or killed.
"Tonight with deep regret Translink has had to suspended some services in Belfast due to ongoing disturbances.
"Thankfully no one has been hurt in this incidence, but those responsible for this attack, and ongoing attacks on the police, need to stop and stop now.
"I appeal for calm and call on those destroying their own communities and those fanning the flames to end this recklessness before someone is seriously hurt or killed."
Translink chief executive Chris Conway condemned the attack on the company's staff member.
He said: "Thankfully, all passengers got off the bus safely before the attack occurred. My thoughts are with the driver who is badly shaken but thankfully unhurt, he is being supported by colleagues.
"We are working closely with the PSNI and services have been suspended in this area and in other parts of the city. They will remain withdrawn until it is safe to reinstate them.
"Our staff have been working on the frontline throughout the Covid-19 pandemic to keep essential services operating and to keep communities connected, and this attack is reprehensible."
Police are advising members of the public to avoid these areas.
"We would appeal to those with influence in the area to use it to help restore calm," a PSNI statement said.
Irish Foreign Minister Simon Coveney branded Wednesday night's events "disturbing".
He said: "Further very disturbing scenes this evening in Belfast. Attacks on police, journalists and citizens must be condemned by all.
"There are peaceful, democratic and legal channels to address all issues and concerns. Calm and positive leadership needed from all."
Labour's shadow secretary of state for Northern Ireland Louise Haigh said the "mindless violence" is damaging local communities and "serves no purpose."
She added: "The frontline police officers and all those trying to restore calm deserve our support.
"All those with responsibility for Northern Ireland must be united in condemning the violence and coming together to bring it to an end.
"Violence will do nothing to resolve the complex challenges facing Northern Ireland - that will only happen through engagement and constitutional politics."
Videos circulating online show a bus being pelted with petrol bombs and having its windows smashed where a crowd of people had gathered.
Translink Metro said it had withdrawn all services into the area until further notice due to road closures, as well as services in east Belfast.
A crowd of around 500 people, most of them adults, gathered on the corner of the junction at Lanark Way as events unfolded.
Further down the road a bonfire was lit where a crowd of approximately 100 people, mostly young, were assembled.
The Stormont Assembly is set to be recalled on Thursday morning for an emergency debate following days of violence.
Riots and attacks on police have taken place repeatedly throughout the last week and have now resumed after a relative lull on Tuesday.
Police were attacked during another night of violence in a number of loyalist areas on Monday.
Nine officers were injured in Ballymena, taking to 41 the number injured in disorder across Northern Ireland since last Friday night.
The most intense clashes on Monday were witnessed in Ballymena, when nine riot police officers were injured after they intervened in an unlawful march of loyalists through the town.
During the unrest, debris, including a wheelie bin, was thrown onto the M2 motorway, forcing its closure.
Disorder also flared in parts of Carrickfergus, Newtownabbey and Londonderry on Monday, with petrol bombs and other missiles thrown at officers.
Children as young as 12 have been involved in some of the violence that has been witnessed in recent days.
Cars, a JCB digger, a phone box and bins were set alight in the Waterside area of Londonderry on Monday.
Police said that a brick was thrown at a taxi, which was carrying a passenger at the time, on the Limavady Road.
The cause of the unrest has been attributed to frustration over a decision not to prosecute members of Sinn Fein over alleged coronavirus regulation breaches at the funeral of republican Bobby Storey.
Opposition to the Northern Ireland Protocol and drugs seizures against a dissident faction of the UDA in south-east Antrim have also been blamed.