Game creator himself answered another question about this card, but I think it applies here as well.
I think you may have mis-read the text on Secretly Bitten. It says to 'Select a Random Hero'. You could not choose which Hero to play it on, it must be determined Randomly. The regular Zombie card Infected lets you play it on a Specific Hero, but only if you just beat them in a Fight.
Selecting a Random Hero is covered on p.16 of the Timber Peak Rulebook.
Hope that helps.