The 22-year-old students, of Slough, Berkshire, were in London and boarded a Metroline bus from Russell Square to Paddington on Tuesday.
But they said when they presented their tickets the driver told them they were a “threat” to passengers and ordered them off the bus.
An investigation has been started by the firm as a matter of “urgency”.
The pair, who have made a formal complaint to the bus company, have asked the BBC not to reveal their full names.
Yasmin, who was wearing a hijab, and Atoofa, dressed in a niqab - which covers the face - were in London to hand in university work and would usually have taken the Tube, but because Yasmin’s feet were hurting they opted to travel by bus.
Yasmin said at first she boarded the bus by mistake when it was not in service to ask if it was going to Paddington station, but was told by the driver to get off.
“My gut reaction was just to laugh because I thought it was hilarious to be told to get off the bus,” she said.
"About 10 minutes later… the passengers started getting on. When I went forward to show my ticket he said, ‘Get off the bus’. I presumed he was still angry because I got on the bus before.
“He said, ‘I am not going to take you on the bus because you two are a threat.’ I realised it wasn’t due to me getting on the bus, this may be a racist attack.”
The student said the driver told her and her friend that they were a “threat” to both him and his passengers.
She asked for his contact details but when he refused she began to film him with her mobile phone and he covered his face with a magazine.
"I said, ‘it’s OK for you to cover your face on my recording but it’s not OK for my friend to cover her face out of choice?’
“There was no point arguing with him, we got off the bus and by then my anger turned into emotion. I stood there and my gut reaction was to cry.”
notice how BBC states it was because of the veil? in the story we can clearly see the reaction was towards the hijabi first. do you UK people have redneck drivers like we have here?
I think the reason it angers me is because from where I am, I have never seen a hijabi/niqabi struggle with people like that bus driver.
It makes me thankful for the diversity in my area.
This is really sad...and no1 spoke up for them? Ugh..
I was going to say the exact same thing, I really don't have the patience for racists and bigots. I'm so glad I live in such a multicultural area. ...that being said this incident happened in Slough which is pretty diverse. I guess you get idiotic bigots everywhere...
Hijabi are ok...Niqabi...I hate them so much that I feel like taking a match and setting them on fire when I see them
Hundreds of Syrian teachers wearing the face veil were dismissed from their schools as the Ministry of Education said they undermine the secularism of the state, according to press reports Tuesday.
Brother cricketblaya bin teresanam, where is your outrage and maatam over Syria’s very recent and widely enforced government ban on the niqab?
P.S. when will you leave the evil west and go live amongst your kind, pal?
