Sharked,
The following are merely the suggestions and recommendations of a demented old man.
Length: mid 30ft to lower 40ft range. Depending upon the internal layout and number of staterooms, you may accommodate 2 to 4 people in reasonable comfort. Most mid 30ft boats usually allow to reconfigure the saloon table and seats to accommodate 2 people.
You do not want a "wet head" so that means a separate shower within the head.
Pretty much any boat can make it to the Bahamas and beyond assuming you watch your weather window.
I suggest you check the following site for sizes and models then start hunting for a used one. Good luck searching. They are few and far between.
https://www.americantugs.com/models/
Just a bit of information; although my boat is documented as a AT34, it has the same hull as the current AT36. Seems most every boat builder decided to add in the swim platform so as to get more money, selling it as a bigger boat. So far, I have not found anyone willing to live, eat and sleep on the swim platform. SMIRK
As with any boat, you want to investigate the available storage. The hanging closet and drawer space is important to a lady. If you select wrong, your clothes could end up in a shoe box. My lady now has 3 out of 4 drawers in the owner's stateroom. I tried to explain the '1/2 closet' to her but she kept on 'forgetting' until I put a hose clamp around the closet rod. LOL
Now we have to discuss the 1/2 floor space in the closet. LOL
If you travel down the east coast on the ICW, stopping at interesting towns and small cities, it could take most of the summer months and then some. OR do half to the Great Circle...... around the Great Lakes and down the Mississippi River. The key is to get out of the Great Lakes before the water gets 'thick'. THEN two options, across the Gulf, either to the FL Keys or take the cross FL canal. The cross FL canal will put you on the east coast of FL smack dab in the middle of FL.
NOW, that's the extend of the travel brochure. There is a Great Circle organization that will guide you in your quest. Of course if you have your heart set on visiting the Bahamas and beyond, careful planning is necessary. Once there, fuel and fresh water will be at a premium. If you install a water maker, that leaves only finding and managing your fuel.
Good luck in your search. No one says you must buy a boat within a year. Look at LOTS of boats of different styles etc.
Charter a boat, if possible, that you are considering.....
I say the following, "tongue in cheek."
Two subject not to broach unless you wish two start a worthless argument again are, what type of anchor and one or two engines.
Those subject have been discussed many times. You can look at the various topic and follow the blood trail.