The city actually tried that and it failed...
http://www.ocregister.com/articles/bike-383621-bicycle-center.html
OK, if you do find a bicycle to rent, what to do with it?
As far as I know there are two main Bike Racks for guests at the DLR.
The closest is the current Transportation Hub (east side) outside of security next to the ART Ticketing Machine.
And just north of the ESPN Zone at DtD.
So you would need to both rent a bike, but also a good lock.
Is it doable, yes...
In fact, I use my bike to get to Knott's Berry Farm on occasion (I live here, and own my bike and a good lock).
But never have used it for
Disneyland, even though it is about the same distance, partly due to the traffic in the DLR area.
Now, the OCTA Bus system have bike racks, but only two bikes can be loaded on a single bus, and the main bus route (43) seems to always have a full bike rack.