I am not totally sure about how the bus system works but maybe this is useful information.
https://www.visitstmaarten.com/st-maarten-st-martin-bus-routes/I would assume it's not the most time efficient way to get from one side to the other but it would be a local/affordable experience I am sure!
Most of the beach bars on Orient beach have great bartenders/bar setups so I am sure its pretty easy to get a great Margarita if one wants.
Regarding Simpson Bay Beach to Maho, the beach ends and you cannot walk on the "sand" the whole way. Just walk on the road you see on google maps next to airport and you arrive at Maho beach.
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