I found these boards so helpful when I was planning my recent cruise that I wanted to give back. Bimini is unlike any port we've been to, and we loved it. We visited last week on Celebrity Infinity.
For background, we seldom book excursions because our son has some health issues. We use the mantra "maximum flexibility" when getting off the ship with minimal expectations of being able to do too much. We were pleasantly surprised in Bimini.
After reading excellent advice from @lazydayz, @kathynorthand others on these boards, we decided to rent a golf cart and go to Radio Beach. As others have said, you can get on the free tram (some are wheelchair accessible) and go right to the stop where you rent golf carts. We decided to walk down the pier, which was lovely. The most exciting (scary?) part was seeing four sharks circling right off the pier. I had brought my snorkeling gear hoping to get into the gorgeous water, but changed my mind pretty quickly after that. Right after passing by security there is an information booth straight ahead. As we were heading over to inquire about golf cart rentals, a man approached and offered to rent us one: he would go get it and bring it to us. That sounded good, and I asked the info person if he was legit and she said yes. He wanted 80 dollars but took 60: CASH ONLY. No idea what the company was but he said his name was Humpy?
A word about the golf cart: we got a 4 seater for the 3 of us, but we needed to strap the wheelchair in the back (my always thinking husband brought bungee cords). So that meant the three of us squeezed into the front together, which was doable but very tight. Also the steering wheel was very loose; my husband found it tricky to navigate on the busy streets. Humpy provided a map, which came in handy when we got lost. We drove all the way to the end of the main road thinking that was Radio Beach. It was lovely and private but not at all accessible--a steep incline to get to the beach, and no services that we could see.
The North end of the island is Resorts International (left off the pier). We drove through just to check it out, but spent our time on the south end of the island (right off the pier). There are two streets that run parallel to each other on the south end. After you pass through the straw market on the main road, look for a decent road on the right to head up to the road that runs along the beach. After passing the high school on the left, you'll come to some unassuming buildings on the beach, including CJ's and Conch Fu. You can park there and head to the beach in front (Radio Beach) or just find a nice shady spot on the deck overlooking the gorgeous water, which is what we did. This is a local place and rustic; it's not 4 star but it's better: it's authentic.
We had delicious frozen pina coladas in coconut shells (15 each but worth it) and yummy conch fritters from Conch Fu for 6 dollars. Everything is cash only here and it's somewhat confusing figuring out who to pay for what, but the people were very friendly. There is a bank with an ATM nearby that gives Bahamian dollars; we got change from the beach bar in US dollars, which was nice.
Next time, we will bring more cash, head straight to Radio Beach by golf cart, and maybe I will even get up the courage to snorkel there.