I've been stopped at the gates with my folder at Bank, until I folded it. I'd be very surprised you could board in central London with a full sized bike on the lines it's officially banned (eg central line, DLR)
It is not officially banned to take a bike on the Central Line. You can only travel between specific times. I do it at least once a month and the TFL PDF image @ianrauk provides in this thread clearly shows this as well.
Bank station has restriction for cycles based upon accessibility & the gap between the platform and train on some services.
You can neither board a train with an unfolded bike at this station or permitted to depart at this station with an unfolded bike.
Bikes are also permitted (not banned) on DLR which you can discover with Google.
http://lmgtfy.com/?q=Bikes+on+dlr
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