If I use Virizion's "Bail Out" attack, can I choose to put zero Pokemon into my hand if I have any Pokemon in my discard pile?
No, if you choose to do the attack and you have a Pokemon in the discard pile, you have to choose at least one of them. But remember, you can always choose to pass and not attack.
Source: Fusion Strike FAQ; TPCi Rules Team (2021-11-11)