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Check with other airlines as you will have to transit through another country then fly on to Bermuda.

You will need transit a transit visa. and a visa for Bermuda.

Do you have a job to go to and do you have accommodation arranged or money to pay for it.

What I have done on that issue is that I was advised by my employer to get a transit  or multiple entry re entry Visa via and specifically a Direct Airseide Visa such that I dont pass through  the UK border control and I have secured that Visa now. From my research it is much easier to transit  via UK than USA or Canada.