What is needed for Bitcoin to become the reserve currency of the world? Bitcoin's characteristics seem to make it a prime candidate as a reserve currency, given it has fast transactions to anywhere in the world at a low cost with little to no price manipulation or export/import controls.

Imagine a traveller arriving in a foreign country, having bought 100 Bitcoins in his country. Rather than go through a middle-man currency exchange, he finds someone who wants Bitcoins (or even a Bitcoin ATM) and sell his Bitcoins for local currency.  When he is ready to leave, he simply sells back his local cash for Bitcoins without being hit twice by the currency exchange's transaction fees.

What would have to happen to make this a reality?  Is it feasible?
You would be hit twice by the currency exchange anyway if you were to buy Bitcoins for your local currency, and then buy the foreign currency with Bitcoins. If you would perform those transactions at exchanges ran by large companies, there is little difference from a traditional model. If instead you would use exchanges like Mt.Gox, the spread would go back to the people, rather than a company. The spread might be smaller or bigger, it all depends on the market.
Banks and companies like Visa often allow you to withdraw foreign money at a local ATM in the foreign country, sometimes even not charging you anything for the operation asides the money conversion spread. You perform only one conversion for the bulk of your money, and whatever is left over you can sell back at the money exchange. So by bypassing Bitcoins, you can save money (if the banks operated at a comparable margin as the Bitcoin exchanges, be they owned by a single company or not).
Most Bitcoin exchanges offer you money withdrawal to a bank local to the currency. If you were a tourist, this would not be convenient for you, as you wouldn't have an account in any bank like that. An alternative would be a service like OKPAY, but as it is to handle both Bitcoins and other currencies, there is no need for other exchanges.


So all in all, your proposed idea does not seem to be plausible at the moment. Main advantage of using Bitcoins for such a task is lowering the spread, which could also be accomplished without Bitcoins (say, an online community currency exchange). The proposed idea would however be more plausible if a whole country would adopt Bitcoins as its official currency, which is very unlikely to happen in the nearest foreseeable future (governments seem to move away from currencies tied to a limited resource, like gold or silver, to fiat currencies to enable easier growth).