I have done many Gulf Stream crossings from Florida to various parts of the Bahamas. I have done it with only a compass and a knot meter (no GPS or RDF) and dead reckoning and also with fancy chart plotters. Of course GPS is the way to go and one hard wired into your boat at the helm, in my opinion is recommended (I like Garmin) and it is a good idea to have a back up hand held too (I like Garmin). But depending on existing electronics and whether they can talk to each other, might dictate the make you choose.
Of course any safety gear required in the US is required in the Bahamas (life jackets, life rings, flares, etc.). That's a no brainer.
Don't forget your passports and don't forget to clear customs upon landfall. And if you anchor in the Bahamas at night, before you can clear customs and immigration, then fly a quarantine flag. It is also a good idea to have the Bahamian flag to display while visiting the country to show your appreciation.
Someone mentioned Explorer Charts. By far they are the best chart books for the Bahamas. That is great advice.
Obviously you want a good VHF Marine Radio with an antenna mounted on the mast. Not for necessarily chatting with others, but to get up to date weather reports. It is essential that you watch the weather and go when there is a good window. The Gulf Stream can get very nasty with unexpected cold fronts at certain times of the year (like now) and you can get spanked bad if you don't watch out. It's no fun to be sea sick or have to deal with others who want to die because of it.
If you have radar, that is cool, but don't go out and buy one for this trip unless you can afford it and have the time to install. Not necessary. A good depth sounder is essential. You will have to learn to read the water by color so you don't run aground or even worse, run aground on coral. But the depth sounder keeps you abreast of having enough water under the keel, because it can get shallow in many parts of the Bahamas.
A good anchor is essential with proper ground tackle (chain & rode) and a 2nd anchor is advised in case you lose the first one (or two so you can anchor in different type bottoms). Some think you should use two anchors when anchoring in the Bahamas. If you use two anchors and everyone else in the anchorage has one anchor, you will tangle. Everyone should do the same thing.
It is a good idea to bring some fishing gear so you can troll for fish while underway. What to get and how to use it and what bait to choose is another topic. But, one of the great things about the Bahamas, is living off the ocean. Once in the Bahamas you will get a cruising permit and then you can bring yourself up to date about their current laws on fishing and taking lobster.
Bring clothes for warm weather and cold weather. For dry weather and wet weather. You could experience it all. Especially in the middle of the night if you passage make after dark.
Obviously have enough food and fresh water to last in case you are stuck somewhere. If the weather is bad (it can be hot and sunny, but the seas not kindly), then it is a good choice to stay put until things settle down and you need to have enough things to eat and water to drink.
Of course enough fuel in case you have to motor a long way when there is no wind.
This is all off the top of my head. Obviously you need to have tools on board to fix stuff when you break it.
And a dinghy and outboard is almost essential if you intend to hunt for lobster or go into shore to investigate. If you are going to hunt for lobster and glass bottom bucket is a good tool along with an Hawai'ian sling (but check the laws and sometimes they are allowed and sometimes not and sometimes allowed if you ask that it is written in the cruising permit). Snorkle, mask & fins of course. Remember some coral is really sharp as are some forms of rock. A guide to salt water fish is helpful if you are new to that sort of thing so you know what to also spear with your Hawai'ian sling for eating.
Have fun and be safe.