The 21-year-old backpacker, from Worthing, in Sussex, was last seen in the early hours of Thursday at a beach party on the island of Koh Rong.
As the search entered its fifth day, Preah Sihanouk province police chief Major General Chuon Narin said at least 20 people had been questioned – but no arrests have been made.
He said: “We are questioning as many people as possible and we haven’t detained anyone,” adding that he feared Ms Bambridge may have drowned.
Reports say some of those being questioned are believed to be bar workers on the popular tourist island.
Ms Bambridge’s bag was found with money and a mobile phone still inside on a rock near the water’s edge on Police Beach and her passport was found in the room where she was staying.
Police say the phone shows she posted photos online until 3.23am but her movements after that time are not known.
Mr Narin said the search had been expanded to cover nearby islands and farther offshore in the Gulf of Thailand on Tuesday.
About 150 people have joined the search for Ms Bambridge as divers, navy and police were drafted in.
Both local and foreign volunteers are also helping, while local fishermen and neighbouring provinces in southwestern Cambodia have been alerted, police said.
Ms Bambridge’s mother, Linda Schultes, father, Phil Bambridge, and brother, Harry Bambridge, have travelled to Cambodia to help with the search.
Her father has said he fears she has been abducted.
He told Sky News: “I think someone’s taken her. I don’t think she’s had an accident. If she’d had an accident she would have been found by now.”
Ms Bambridge set off on her trip on 27 September, when she flew to Vietnam, her family said.
They were alerted to her disappearance after she failed to check out of the Nest Beach Club hostel.
During a phone call with her younger sister Georgie on Wednesday, Ms Bambridge said her first solo trip was “doing so much for her confidence” and she was having “the best time ever”.
Mr Narin vowed police would not stop searching for the missing backpacker until she is found.
He said: “We have decided the search mission will not be ended until we find her alive, or her body if she has died.”
Additional reporting by agencies
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