Police Scotland said the additional officers would patrol 24 hours a day on the island, where crime levels are generally low.
Chief Superintendent Hazel Hendren, divisional commander of Argyll and West Dunbartonshire, said “every available resource” was being made available for the investigation.
She said: “I understand that there will be a high level of concern among people living in this close knit community but I want to reassure people that everything possible is being done.
“Incidents such as this are extremely rare but we are still in the early stages of this investigation and we would ask people to be vigilant about their children and also their household security.”
She added: “Additional police officers and other resources have travelled to the island and high visibility patrols have been stepped up, with these additional officers patrolling 24 hours a day. If anyone has any concerns, or has any information, they can approach these officers.
“We also have an incident caravan situated on the island which is staffed 24 hours.”
While Bute has a population of just 6,500, it has long been a popular destination for holidaymakers, notably generations of Glaswegians, and is usually busy during the summer months.
Police Scotland have said they are keen to speak to those holidaying on the island as well as those who took part in the search for Alesha.