Given the diagram, where do I add/replace a larger capacitor for continued power while bike is stopped?
Your guess is right. Placing it on the "left" side of the regulator works well. You can also place it on the "right" side, but then you would need a few extra components (at least one extra diode). It's easier on the "right".

Note: I have to use stupid words like "left" and "right" because the person who drew that schematic failed to add reference designators to the components. Don't be that guy.

A few caveats:


You have to make sure that the capacitor has a sufficient voltage rating. Since you're taking the AC voltage from a dynamo, it's hard to say how high the maximum voltage will ever be. I have very little experience with them. I assume that 6 V is just a "nominal" value, and the output can increase. The peak voltage will be the AC voltage times 1.4, then subtract about 1.6 for two diodes in series (your bridge). $$6 \cdot 1.4-1.6=6.8$$
Now double this (13.6 V), and buy a capacitor rated for at least this much. I suggest at least 16 V, but 25 V would feel safer.
As brhans pointed out in a comment, unless you seriously beef up the capacitance, chances are that you will hardly notice the increased time. This is hard to say without knowing the expected load. The drawback of using a silly amount of capacitance (part from the obvious: cost and size), is that you will get a slower start-up time; it will take time to charge up the capacitors.