Can the Bishop select a player who discarded the Handmaid?
No, the Bishop cannot guess the hand of a player who discarded the Handmaiden last turn. 

This comes from the original rules:


  If all players other than the player whose turn it is are protected by Susannah, the player must choose him- or herself if possible.


This shows that the Handmaid doesn't only cause the player to not be affected, but it actually stops another player from choosing that player when choosing a player.

Also, having to reveal whether or not you hold a specific card is definitely being affected. If you are ignoring all effects from other players cards, then you would ignore the part where you must answer whether or not you have the guessed card.