I made this affect all Zombies because it feels better for the flavor. In current Magic, most effects like this are relegated to only you, so there's no feel bad moments when your opponent utilizes it better than you can. My problem with this version is that getting bit by a Zombie usually causes you to die eventually. Maybe there could be a few of these types of creatures that work together with infection counters to create the whole scene. I'll make a few more in the next few days to show what I mean. Here's a second version that's a bit simpler:
A bit more text-y, but it conveys a different feel. This one is uncommon because it's a bit less complex. The thing I'd like to fix about this one is the fact that if the creature dies during combat, it doesn't become a Zombie.
Let me know which one you like better, or feel free to post a different version that does something similar with better wording.