"Go green, get fit and avoid traffic all at once!" - Miami Marlins
While I strongly feel there's a need for better bicycle facilities surrounding the park (sharrows, bike lanes, etc), I still believe bicycling to the park is the best way to avoid traffic and parking woes. According to the Marlin's website there's bicycle parking stations available on the ground level of each of the four on-site parking garages. If you live within 5 miles of the stadium, I encourage you to get on your bike and give it a try.