The August 2015 bombing left 20 dead in the centre of the city in an unprecedented attack on the junta-ruled nation.
The two accused, Yusufu Mieraili and Bilal Mohammed, were scooped up by Thai police in the days after the bombing and have been held in military custody ever since. Both deny the charges.
Thursday's delay added a fresh layer of farce to a case that has been marked by official obfuscation, with police unable to offer a convincing motive for the attack, according to analysts.
More than a dozen ethnic Chinese tourists were among the dead when explosives -- apparently left in a backpack -- detonated in a Hindu shrine popular with tourists last year.
The blast came weeks after Thailand's junta forcibly repatriated 109 Uighurs to China, where rights activists says the Turkic-speaking Muslim minority face cultural and religious repression.
The timing prompted speculation that the attack was part of a revenge plot against a country which had been a key transit hub for Uighurs as Thailand's military leaders have grown closer to Beijing.
Thai authorities have rejected the theory and insist the attack was in retaliation for a crackdown on a people-smuggling gang.
On Thursday a court-appointed translator -- a female Uzbek immigration detainee -- was turned down by both defendants.
"I can understand (the Uzbek) translator... but not well," Yusufu told the military court in English.
The military prosecutor had earlier refused a translator provided by the defence, according to a judge, who told the court that "the case is a security matter... so the court provided a translator from immigration (detention centre)."
"The court will seek a new translator and postpones the case to October 13 and 14," the male judge, who can not be named, added.
The case was first delayed in August when the translator for the accused, another Uzbek national, fled after he was hit with drug possession charges.
Sirojiddin Bakhodirov accused police of planting drugs on him as punishment for helping Thailand's Uighur community -- a charge officers denied.
"Getting proper translation is a serious matter and not easy for any court," Sam Zarifi, of the International Commission of Jurists, told AFP.
"But this is a very high-profile case for the Thai government and they've had months to prepare so it's unclear why they can't provide the necessary translation, while the suspects are being held without a trial."
Prosecutors accuse Mohammed of placing the bomb inside a backpack at the shrine and say Mieraili was involved in transporting the device.//AFP