I don't know enough about motorcycle electric circuits to understand for sure what you are trying to do, and you should be ready to discount this post, but I would guess that you really want to replace everything so that it's all 12V (generation, storage, and consumption), rather than having parts of the circuit 6V and using a doubler to convert that to 12V. Maybe a voltage doubler is a standard way to deal with this problem, but I would make sure of that before proceeding.

Are you leaving the ignition system at 6V and only converting the lighting circuit?

As far as your question about current goes, if the power consumption is constant, then doubling the voltage means cutting the current in half. However, there is no guarantee that 12V lights consume the same amount of power as 6V lights, so there is no way to know if the current cuts in half or not without more information.

If you do end up building a voltage doubler, be aware that some automotive circuits use MUCH more current than typical electronic circuits, so you need to make sure you use components that are rated to handle whatever current they will be carrying. If you get components that can't handle the current, they will melt in a flash of light and a puff of smoke (which is pretty cool to witness if you didn't invest much time or money in them ).

Sorry that wasn't much help. Do you have access to a motorcycle mechanic? They would probably be more helpful than an electrical engineer.