She was following the same route as her brother, Muhamet Ismajli Syla, who died with seven other members of their family in the Racak massacre on 15 January. His body and those of 39 others were seized two days later by Serbian security forces and taken to the morgue at Pristina hospital, 18 miles away. Now she was going to bring his remains home - or so she thought.
Bedrije herself had not been to Pristina for seven months. Kosovo's ethnic Albanians are fearful of making such journeys, during which it is quite possible to vanish. The relatives of the 45 victims of Racak have lived, since the massacre, in near-complete uncertainty.
"We just want an official statement from someone, but we've heard nothing," said another member of her family.
But the local branch of the Democratic League of Kosovo (LDK), the main Albanian party, had announced that the relatives of the dead should assemble yesterday morning in Stimlje, the main town in the district, and go up to Pristina in convoy to collect the bodies. It had been on the TV news from Albania: everything must have been arranged.
"We want to bury them all together in a special place, and name it the graveyard of heroes," said Bedrije as the convoy, accompanied by carloads of international media, arrived at the morgue. The relatives stood outside in the snow - grizzled farmers in traditional white Albanian hats, old women in white headscarves of mourning - waiting for someone to tell them what to do next.
Shaban Halimi, a party official from Stimlje, borrowed a reporter's mobile phone. After a while trucks arrived to carry the bodies home, but it began to dawn on everyone that nothing had been arranged. The LDK was evidently hoping that the presence of the families and swarms of television cameras would force the Serbian authorities to give up the bodies, but the doors of the morgue remained closed.
Rumours ran through the gathering as the wait dragged on. "If they won't release all the bodies, I say we shouldn't take any of them," shouted an old man, responding to one such story. Others were thinking of their homes in Racak, which has remained deserted since the massacre. "Some people say there are Serbian policemen living there now," said a villager. "We haven't been there for more than two weeks - who knows what is going on?"
The LDK's tactics worked to the extent that Michael Petersen, a human rights official of the Organisation for Security and Co-operation in Europe (OSCE), which is monitoring the ceasefire shattered by the Racak massacre, arrived on the scene. He and two representatives of the families went into the morgue to negotiate with Serbian officials, but hope was ebbing among the families, despite the efforts of Bedrije, who was urging everyone to stay "until we get the bodies back".
Her anger grew when Mr Petersen emerged. "We want to make sure that the funeral is carried out in a dignified manner," he said, "and we have agreed that with the help of the OSCE, the relatives and Serbian and Albanian authorities, it will be organised to everyone's satisfaction." He would be having further meetings with Serbian officials, but word was that it would be another two or three days before the dead of Racak could be laid to rest.
"This makes me think that Europe is intimidated by Serbia," said Bedrije. "Europe should be ashamed that women have to come here and be treated like this, waiting five hours in the cold." The general mood, however, was one of resignation and she climbed reluctantly into a car to go home.
But then, in an apparent reversal, the Serbian judge Danica Marinkovic said the families could take the bodies.
There was to be more haggling ahead. When the families returned to Pristina they insisted the OSCE organised the hand-over of the bodies and the burial because they feared Serb harassment. "We are afraid," said Hafiz Mustafa, one of the relatives.