You can basically ride North or South, not East (obviously) nor West (there's no bike lane to take you over the bridge.)
If you'd like to do a circle there's a couple of trips you could make.
1. North: Ride about 4 miles until just before you get to the water. On the left is an entrance to a small park. There are rest rooms there if needed. The road there (hard gravel/dirt) goes all the way back south to SR510. It's named Jungle Trail and when you get to SR510 just turn East to get back to Disney.
2. South: Ride about 2.5 miles. Make a right turn on the main street. (It's the only street you'll actually cross as everything up till then is just driveways into different resorts.) Follow the street West for about 3/4 mile, and it will then turn North, and becomes the road Jungle Trail. It becomes dirt/gravel, as it goes along the edge of the water. It eventually meets SR510 (just across the street from where you exited the northern section of this road, as explained in #1 above.) One nice thing is just before you get to SR510, there's a small park on your right. I believe it also has rest rooms. Anyway, you can walk/ride into the park follow some trails there. The condition for riding those dirt trails might vary a lot, almost needing a mountain bike. Or just rest, then follow Jungle Trail back to SR510, turn right (East) and get back to Disney.
3. The pelican wildlife refuge mentioned by the previous poster is located along Jungle trail, in the loop explained in #1 above.