As the others have said, Bahamas is an easy run and every boat on this site can make that trip. Bermuda introduces additional challenges. The biggest is range, distance and time. If you have the fuel capacity to make the trip, on most boats you're still talking about 80 hours or so. If you look today, you'll see 3' at 6 seconds off the coast. However, by the time you reach Bermuda you're into 7' at 8 seconds. Let's watch that system clear by the 28th and you're down to 5' at 6 seconds. By the 29th you're at 3' at 7 seconds, looks wonderful, but it's 5' at 5 seconds off the coast so rough start. Just with the distance to Bermuda you're talking typically very different conditions from the start to the end of the trip. You're also talking long enough periods that changes to the forecast may occur. Now take that to Hawaii and you're several times what you face going to Bermuda.
Just a simple safety factor. You break down between the US and Bermuda and you can still get a tow, even covered possibly under your membership. Not ideal. Takes time. May leave you uncomfortable for a while, but on their way. When you're hundreds of miles off shore, all that safety factor is gone.
There is a reason in Captain's licensing that there's a Near Coastal license that only covers 200 nm from shore and an upgrade required to go further. Once you get over 200 nm from shore you face a whole new set of challenges that can put your seamanship to a test, more even than the boat. Still you depend on the boat and it requires a different boat.
Boat needed is a combination of design and size. The smaller the boat, the more critical that it meets all the criteria of being an ocean going boat. Above a hundred feet, nearly every boat will. In between, many questions. Definitely limited builders as mentioned above building passagemakers.