Officers said DNA found at the scene led them to Georgiev, who reportedly went to work in a vineyard hours after the alleged murder.
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The Yambol District Prosecutor said an investigation into her death is underway.
The arrest of the suspect was announced two days earlier by Prime Minister Boiko Borissov.
Press reports say the 67-year-old woman was killed in the village of Malomir, 200 miles east of the capital Sofia, where she lived with her husband.
The following day, her body was found, extensively burnt.
Mrs Bennett, 67, moved to the village of Malomir in Bulgaria from Turkey three months ago with her disabled husband Nick. His most recent prison term ended in December 2012, BTA said.
Bulgarian media originally reported that the attack on Bennett may have been a robbery gone awry, with an initial examination showing the pensioner had been struck on the head by a blunt object, as well as her assailant’s fists. She had last been seen taking her dogs for a walk.
Mrs Bennett’s 62-year-old husband is understood to have been admitted to a local hospital where he was being treated for shock.
Bennett’s two dogs were not believed to be with her at the time of the attack, as reported elsewhere, and the animals are now being cared for at kennels nearby. “I will miss your amusing comments, your kind words and your never ending enthusiasm and joy”, the Daily Telegraph quoted her as saying.
She and her husband had been popular members of the expat community in Altinkum and were active members of a local church group there. Bless you Jan.’.
Bennett’s brother was on Monday travelling to Bulgaria from the UK.
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A memorial service is being held in Turkey on Sunday in Mrs Bennett’s memory, and friends have paid tribute to her online.
