The "Bite" action can only be performed on the user's own eggs. A user who owns an adult Vampire can use the Bite action to attempt to transform the egg, though there are risks. The egg might be killed by the Bite action, or it may successfully turn but the other dragons become "repulsed" by it and it is automatically abandoned.
Personally, I tend to use Bite if I don't have much I'm hunting for a the time, and if the AP is full of a single breed. I'll grab a few random eggs and see if I can get any Vampires :D
If you'd like one, let me know and I can see if I can make one!