Go through your results for flights to Bermuda in Bermuda with Netflights. Although American Airlines usually has the best prices, it's best to double check what's available for your travel dates.
If these flights are too expensive, try searching for a different time of year. So if your dates are flexible, consider looking at different times of year.
Look out for flights with American Airlines, as they often have good deals. Or broaden your search by looking at other airports in Bermuda.
For even more options, check what other airports you could fly to Bermuda from. You might be able to make a saving by going from a different airport or city.