First of all, it depends on where you are staying. The answers could be better explained if you identified this first.
But, in the meantime, if you are staying on the French side, then I would recommend taking a taxi if you will be drinking at a beach far enough away from where you are staying. If you are on the Dutch side, then it would depend on where you are staying because if you are staying in Maho or Cupecoy such as the Towers or The Cliff and Rainbow Beach Club, then you could easily walk to Mullet Beach. If you are staying at the Sapphire, you could easily walk to Cupecoy Beach or a longer walk to Mullet but doable if you enjoy walking. If you are staying in Simpson Bay such as the Pelican area, then there are beaches there you could walk to (not the greatest but beaches none-the-less). There is also a great beach area to go to called Karakter's and it's located next to Mary's Boon. You could spend the day there and it would only be a short cab ride to and back BUT you would need to tell the driver to pick you up as they don't hang out there. No bus travels inland. They usually stay only on the main road.
If you are determined to go to Orient from the Dutch side, I would recommend taking a cab so you can drink as much as you like without worry.
It's refreshing to get a question such as this because most people who drink while on the beach don't even concern themselves that they will be driving and possibly causing an accident or worse. The combination of sun, alcohol, and not being familiar with the roads can play a big part in response time so thinking ahead is the mature and responsible thing to do. Good for you!
The bus system on the island is convenient for daytime hours (on the Dutch side)and so if you are staying in the Simpson Bay area, you can easily take a local bus (more like a mini van) to Mullet for about $1.00 each way per person. Just walk out to the main road and wave down a bus going in the direction of the airport with a sign in the window that says Mullet. And on the return, wave down a bus that says Philipsburg. Just make sure to tell the driver when you would like him/her to stop. Otherwise, they just keep driving. Taking the bus from Cupecoy, Maho or Simpson Bay to Philipsburg is the best deal on the island! I do it now all the time and truly love it. No parking, no worries, no hassles!
Hope this helps a little but it would certainly be more helpful if you revealed where you were staying.
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