US President Donald Trump caused a political storm last month when he called for the withdrawal, saying that the battle against the Islamic State armed group (IS) had been won.
He has since rowed back, saying the withdrawal will be done cautiously.
Tensions erupted ahead of the Ankara talks after Bolton said the retreat was also conditional on the safety of US-backed Kurdish fighters – considered terrorists by Turkey.
Ankara immediately hit back at his claim that it would target Kurds.
Recep Tayyip Erdogan said Turkey was the only country with the power and commitment to stabilise Syria after a US pullout, in an opinion column published in the New York Times on Tuesday.
The Hurriyet newspaper reported that Turkish officials were asking for Washington to either give Turkey all of its bases in Syria or destroy them.
The Kurdish media outlet Rudaw reported that Bolton conditioned the talks on Turkey agreeing to protect the Peoples' Protection Units (YPG) in Syria – which Ankara says is linked to the Kurdistan Workers' party, a group designated by the US and the European Union as a terrorist organisation.
Meanwhile, Mike Pompeo, the US Secretary of State, also fell foul of the Turkish leadership when he said Washington will ensure Ankara does not slaughter Kurds in Syria as American troops withdraw.
His comments came ahead of his arrival on Tuesday in Jordan on a Middle East tour. Pompeo said that IS would not be allowed to regroup, following a string of battlefield defeats.
After setting off on the trip to eight Arab capitals, Pompeo told reporters: "The United States is still committed to all the missions that we've signed up for over the past two years."