Usually what happens is, when you are first exposed to the virus and you get infected you have a cutaneous manifestation (the bump on your skin) within a few weeks. But it can be delayed. You can have it within a few weeks or there’s a latency period of up to 12 months. This means that your body may not show signs of infection during that period.
So, you can be exposed to someone with a wart, get infected by the virus, and not develop a wart for up to a year which makes it really hard to figure out how you were infected.