1) Bicycles are allowed on WDW highways/streets.
. . . WDW streets are permitted
. . . WDW resort roadways are permitted
. . . WDW resort sidewalks are not permitted
. . . DTD sidewalks are not permitted
. . . FW has roads and bike paths for riding, plus bike parking areas
2) However, no bike parking near the theme park entrance.
3) You can park a bike in the park's car lots, near the motorcycles.
4) There is a cage/stand for bicycle parking and locking.
5) But, no parking near the International Gateway entrance to Epcot.
NOTE1: Most who use their own bikes at WDW keep them in their resort room, as there is no resort parking area for bicycles. This avoids theft, but also makes for a crowded room.
NOTE2: There are many CM's that ride their bikes to work. Of course, they have a different parking area than the general public. They usually park their bicycles in the same area in which we park our motorcycles (depending upon the building, park, resort, etc).