I fly mostly over water, mostly in the Caribbean and sometimes on very long flights. Yet, I would not chance your 6 hour trip.
Are you sure there is no avgas? The airport's web page for general aviation (
http://www.bermudaairport.aero/pages...laviation.aspx) says there is one FBO and various phone numbers, including two for Esso fuel: (441) 505-9314 or (441) 293-1953.
The other alternative, assuming you have a very flexible schedule, is to wait for a winds-aloft forecast calling for strong west winds followed by strong east winds 4 or 5 days later.
When I travel over water I always make especially careful preparations. My "backup" Skymaster website (
www.skymasterus.com) has a whole page on this, covering far more than its title of "Ditching: How to Avoid & Prepare". And in "Weather Websites" you will find an extraordinarily useful U.S. Navy website all the way at the bottom, providing wind, rain and seas forecasts for 7 days.
Ernie