I see no way that a cycle could emerge "from" the Tumbler unless the car was extensively modified (and enlarged.) The body of a cycle would have to go right through the cockpit, which seems infeasible. (It also seems infeasible to have the cycle "below" Batman, since he's practically lying on the ground in the existing prone position anyway.)
Now, here's an interesting suggestion, though: remember the first TDK spy photos of the Tumbler, sitting outside in the Chicago warehouse parking lot? All the body panels were missing. Now, this may be because it was simply being transported, and the external accessories were crated up separately... but what if this were the actual appearance of the car at some point early in the film, showing Bruce modifying it? (Strapping on new weapons, armor, etc.?)
Just a thought!
-- Admiral Nelson