If I were you, I would call the court. It's possible that they may have not yet issued a warrant if you didn't appear. Ask them how to resolve it. You may be able to submit a sworn statement and pay the fine. You can also ask to speak to the prosecutor.
Also, look at this. I don't know if it's dated, but it talks about instances like yours.
http://www.queensdefense.com/outofstatesum.htm
Finally, look at this:
http://www.hsmv.state.fl.us/ddl/faqsuspend.html
"If you hold a Florida license and have received a ticket in another state, they will send Florida the ticket information and it will be added to your record."
I don't know if you received a traffic ticket in NYC, but since bicycles are regulated under the Vehicle and Traffic law in NY, you may have:
http://www.dot.state.ny.us/pubtrans/share.html
If so, you could have problems in Florida since NY and Florida have reciprocity in dealing with traffic offenses. You might be able to find that out by calling the Florida DMV.