If you're looking for a nice, long bike ride, from the resort go through the tunnel to get to the other side of A1A, turn North. Follow the sidewalk for about 3.5 miles. Right before the land narrows and becomes basically causeway, you'll see a small dirt type road to the left that goes to a small park. This is named Jungle Trail. You can follow that road South. It comes out somewhere around 510, not too far from Disney. I've seen bikers and joggers on that road.
If you want to continue, when the road comes to 510, just proceed straight across. It follows the causeway South for about another mile, then becomes paved road and curves East. Continue following it and you'll get to A1A. Turn North and ride the sidewalk back toward Disney.