Cold open to 1943 in Montgomery, Alabama. A black woman boards a bus and is told she must re-enter the bus from the rear. She protests and the driver intimidates her into getting off the bus and then drives off before she can re-enter through the back doors.
Flash to twelve years later, 1955. The T.A.R.D.I.S. appears in an alley. The Doctor looks out and reports back to the Companions that they aren't back in Sheffield yet. Apparently, this is their fourteenth attempt.
The T.A.R.D.I.S. detects traces of time-traveling energy not related to itself and The Doctor decides to investigate. As the group walks through town, Ryan notices a woman drop her glove and tries to return it. Her husband reacts to Ryan touching his wife's arm by slapping him in the face. The Doctor tries to intervene and Graham states that Ryan is his grandson. The man tells them that Ryan will be lynched if he lays a hand on a white woman again. The woman from the bus scene in 1943 appears and seems to appease the situation, telling him that his suit will be finished soon and will look great.
Once the man and his wife have left, the seamstress describes to the group what happened to Emmett Till for talking to a white woman when he was visiting Mississippi from his home in the North. His body was found in the river. Ryan acknowledges that he doesn't want to be the next Emmett Till. She introduces herself as Rosa Parks. The Doctor tells her that she's a big fan, confusing Mrs. Parks. As she walks away, The Doctor scans her and finds that she's registering the time-travel energy too.
A man finds the T.A.R.D.I.S. and scans it. He's unable to open it so he knocks on the door. He tries zapping it but the force shields repel the shot.
In a pub, the group is discussing Rosa Parks. Looking at a newspaper, The Doctor notes that they've arrived the day before the day Rosa famously refused to give up her seat on a bus. While they're talking, they are drawing the attention of the pub's white patrons, white servers, and black kitchen staff. The waitress approaches them and states that they don't serve people of color, identifying Yaz as "Mexican" and tells them they have to leave.
The Doctor tries to send the Companions back to the T.A.R.D.I.S. for safety but both Yaz and Ryan refuse to walk away from the situation, inspired by what Rosa Parks will do the next day.
Rosa Parks is approached by the man who tried to break into the T.A.R.D.I.S. and he makes her feel uncomfortable although he says that there's no problem at all. She walks away and he smiles.
The Doctor and the Companions follow the energy trail to its strongest point, a building near the bus company. Unlocking it with the sonic, they enter an empty storage warehouse. The Doctor scans with the sonic and a suitcase with the initials "G.F.B." on it appears out of nowhere.
The Doctor opens the case and finds broken pieces of alien technology. Just as she finds a clue to the energy signals, the man from the alley turns up and fires his weapon at them. He chases them outside where they hide by some rusted gasoline tanks. He climbs up to gain a vantage point and The Doctor leaves the group to confront him from on top of another tank.
She identifies his weapon as a temporal displacement gun which is almost out of power. He identifies the police box in the alley as her T.A.R.D.I.S. and hypothesizes it might be worth something. She says it's not but it's better than the vortex manipulator he's wearing on his wrist.
She wants to know what he wants with Rosa Parks. He refuses to answer and instead threatens to kill them the next time he sees them. She calls the Companions to her after quickly scanning the other alien. They walk away.
The group checks into a motel but because it's "Whites Only," Ryan and Yaz have to sneak in the bathroom window.
Graham asks why they can't stay in the T.A.R.D.I.S. and The Doctor says that the alien is watching it so they'll run into him if they stay there.
A police officer named Mason knocks on the door and Ryan and Yaz have to hide in the bathroom. He questions The Doctor and Graham about the whereabouts of a black boy and a Mexican girl, calling them "mongrels". The Doctor denies knowing anyone of that description. He searches the bathroom but there's no one there. He tells them to get out of town.
Ryan and Yaz are hiding behind the garbage bins in the alley discussing racism.
Graham calls them back and they decide on a plan of action. To research Rosa's routine, they board a bus that runs between her work and home. They catch up with Rosa on the bus and talk with her a bit. When she disembarks, Ryan follows to see if he can talk with her more.
Graham is charged with finding the driver, James Blake. Yaz has to put together a timeline. The Doctor will find the other alien and warn him against messing with history.
Rosa spots Ryan following her and asks if he's a spy for the police. He convinces her that he wants to help with the civil rights fight.
The Doctor returns to the bus warehouse and when the alien approaches, she throws his suitcase between them to get zapped by his weapon and displaced into the future. She interrogates him about his time in Stormcage, the most secure prison facility this side of the universe.
He introduces himself as Krasko and admits to having a sordid, violent past. The Doctor reveals that her sonic detected a neural restrictor in his brain which prevents him from killing or injuring any living thing. She demonstrates by ripping his vortex manipulator off his arm and stomping on it. He grabs her but is forced to release her when the neural restrictor kicks in.
She warns him off of interfering with history but he insists that he'll be able to "fix" the course of history.
Rosa introduces Ryan to her meeting group and he shakes hands with Dr. Martin Luther King as part of the intro.
At the bus drivers' pub, Graham discovers that James Blake is taking a holiday the next day which contradicts history.
After the meeting, Ryan tells Rosa that the fight is worth it and thanks her on behalf of himself and Grace.
When Graham relates the information about James Blake not driving the route, The Doctor realizes that Krasko is interfering by just "nudging" history a bit to negate Rosa's influence on the world. To correct the nudge, The Doctor and Yaz arrange for the replacement driver to be flown to Vegas for a Sinatra concert.
Graham and Ryan find James Blake at his fishing spot and hint that there's going to be black passengers sitting in on buses throughout Montgomery that night. Blake rushes back to drive his bus, to prevent them from breaking segregation.
The Doctor and Yaz drop off The Doctor's coat with Rosa for mending. Yaz stays to keep an eye on Rosa until she needs to catch her bus.
Blake finds his bus damaged beyond driving, courtesy of Krasko, but The Doctor and Graham commandeer another bus and deliver it to Blake. Ryan is sent ahead to make sure no one waiting for the bus decides to walk but discovers Krasko has posted notices on the stops that service has been suspended for the night.
Krasko has blockaded the bus route as a final attempt to nudge history. Ryan confronts him and when Krasko comments that preventing Rosa's protest will keep Ryan's "kind" from getting above their place, Ryan zaps him with the temporal displacement weapon.
As the passengers continue to board the bus, The Doctor realizes that she and the Companions have to stay on the bus because otherwise Rosa will not be asked to move. Graham doesn't want to stay and be a part of this history, to witness Rosa's arrest but they do and history proceeds as it should.
Back in the T.A.R.D.I.S., The Doctor gives a quick recount of Rosa's influence on the world and the universe.