There is no city sponsored bus but there are plenty of shuttle services to look into. Try setting up something before hand so that you get the best price.
Yes, it'll cost you 1.50$. Take the bus from fort Lauderdale airport to the tri-rail station. Follow the tri-rial to Miami international airport. And then wait for the south beach bus from there. I recommend using Google maps transit feature, as it can be hard to keep up with the bus schedule at time. But all in all only takes about an hour and a half, and you get to see some of the neighboring city as well. Hope to see you soon!
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