Bermuda tends to be an expensive destination, but Scott’s Cheap Flights has found some fares of $378 roundtrip from Austin. Prices vary by date, but some low fares are available into October 2018.
Check the websites of American, Delta and Jetblue to find available dates.
There are no rivers or natural lakes on Bermuda, so finding fresh water is an issue. Every house and building has a white roof that collects rainfall so it can be stored for use. Think about that as you shower in your hotel in Bermuda.