There have been a couple discussions in the past few weeks about going offshore in small boats that you might want to look at, but in a general sense, anecdotally its easy to find stories of people going offshore in boats that are less seaworthy than the Bayfield 25. But if you read enough, you find that historically lots of small boat sailors went missing, or needed rescue and historically the small boat sailors that took off on offshore voyages were generally very experienced seamen.
When you ask about sailing a Bayfield 25 to Bermuda, its all about risk management and how much risk you personally are willing to take, and how good a sailor you are, and how expeienced you are in handling the Bayfield in heavy going.
To me, a Bayfield 25 would be an extremely poor choice for this kind of trip. These were boats that were optimized to get a lot of room on a small boat, rather than as a good sailing, offshore comfortable design. For example compare the Bayfield to something like a Folkboat with an equal displacement and length but 4 foot draft vs the Bayfields 2'11 draft and 2300 lb ballast vs the Bayfields' 1450 lbs, and the Folkboat's 7'6 beam vs the Bayfields' 8 foot. So, comparatively speaking, the Bayfield with its extremely low ballast to displacement ratio, extremely shallow draft, wide beam carried to its full ends, and corky motion, it would be very tough boat to bring through a storm.
These boats do not exactly have a good reputation for being well constucted. They are heavy but much of thier weight comes in the form of heavy interior components rather than robust structure or ballast.
The Bayfields' high drag and small SA/D would make for a very slow trip to Bermuda, which means that you would need to carry a lot more supplies, than a longer or better designed boat of this displacement. The weight of those supplies would further reduce motion comfort and seaworthiness. The slow passage time would also mean that you would be at sea too long to acurately predict the weather window that you will encounter en-route and that means you higher risk of ending up in foul weather.
But again, while the Bayfield 25 would be very close to the bottom of the list of boats that I personally would consider taking to Bermuda, it comes down to how much risk you personally are willing to take. To quote Clint Eastwood's Dirty Harry, I guess the real question is, "How Lucky do you feel?"