This is actually a very funny and interesting question.
I guess it depends on the type of zombification.
If the victims are entirely aware of what is happening yet can't control their bodies, it would be a nightmare for me and I would CTB before ever taking the chance of being bitten.
If the victim loses all hints of self awareness and is basically just an animated corpse, I'd probably just go about my life surviving from day to day just like I do now.
I think I would fear people a lot more than zombies though, with governments and all being shattered, I can imagine the amount of crazies would increase, with that comes slavery, more thieves and people's true colors truly show when they can get away with it, you see it every time during a crisis, even sweet lil' granny down the street might have a murderous fantasy she wanted to live out.
I trust a zombie more than the living in that regard.