Newly infected should turn within a few minutes at most
The reason for this is to remove any ability of newly infected humans to react. If it takes many hours for a newly infected to turn from patient zero, then the virus will be easy to contain.
Lets say those bitten by patient zero take 2 hours to turn. At first, people may seemingly be murdered by patient zero, but very soon police will be called and the injured will be seen in hospitals. Police officers will easily put down patient zero. Those seen in hospitals will turn, but will be quickly restrained. I would expect any trained physicians to quarantine new victims bitten in the hospitals, thus stopping the infection there. As for those 'murdered' by patient zero outside the hospitals, it will not take law enforcement long to put down the 'murder' victims rising from the scene.
However, if patient zero is in a major population center, and his victims turn in a few seconds, then the cascade of zeds will exponentially increase, completely wiping out whatever continent it was on.
As for how the infection will spread overseas, that has to be left to you. Perhaps a terrorist organization collects some of the victims and unleashes them against their victims. Perhaps one zed strays onto a cargo boat as it's leaving port to safety on a new continent.
"Proof (this is fiction of course)"
Note how every single zombie story with a long (hour or more) period between bite and turn focuses on survivor drama, and starts out with everything 100% apocalyptic from word go. None of these shows or movies ever show from patient zero.
Zombie Land - We get flashbacks to before the outbreak, but no detail about how it's spreading.
Dawn of the Dead - The MC wakes up, everything's in chaos, and she takes refuge in the mall.
Walking Dead - The story starts when Rick wakes up; after the apocalypse.
Left 4 Dead - Story starts after the outbreak.
Dead Rising - People turn slowly, and the outbreak is contained to one town.
The only one that shows me a plausible apocalyptic spread is WWZ. And the newly bitten turn in 8-12 seconds.