I don't know, maybe it depends on the person and the virus involved. But I think you can catch a virus from a person not even showing the symptoms....so a few days I think. I seem to remember my biology teacher telling me that. You only have symptoms because the body has already started bringing up the different defenses and the virus has been starting to do damage.

I know it's not a common cold virus, but I know that for the AIDS virus, a person can be the most contagious when they have it the first 6 months and may not even know they have it.