I am an Indian citizen and I found that Bermuda provides visa-free entry to Indians.
Is any transit-free flight route available?
According to the Wikipedia article on L.F. Wade International Airport, there are commercial passenger flights to the US, Canada and the UK.
Indian citizens need a visa to visit or transit in all three countries. The US and Canada (for the most part) make no distinction between airport transit and other purposes and always require visas for Indian citizens. The UK does but Indian citizens are in the most restrictive category and, unless they qualify for some exemption, they need a Direct Airside Transit Visa even if they don't intend to go through immigration control and leave the airport.
So the answer is that there is no regular visa-free transit route for Indian citizens between India and Bermuda.