I don't know how it is in WWZ (haven't read the book in a long time, and don't recall from the film), but in the Romero movies it works like this:
Anyone who dies from any reason turns into a zombie
The bite of a zombie is venomous, and deadly, unless the affected area can be amputated before the poison spreads (see Day of the Dead)
So, I'd do something like make the zombie bite poisonous, requiring CON rolls to stave off the infection.
Start at CONx7. Fifteen minutes after the bite, make the roll. Fifteen minutes later, roll again at CONx6. Then CONx5, etc.
If the character is bitten again in the interim, immediately have him make the roll again at the next lower level.
And, of course, whenever the roll is failed, the PC starts coughing up blood, collapses, and in 2D10 rounds comes back from the dead.
Of course, if someone dies from any other reason, they'll come back, too.
Please note I do not actually work for Chaosium; I just do the occasional freelance editing work for them.