If my active Pokemon with 30HP remaining has a Rescue Board tool attached, making it have no Retreat Cost, does Ariados' "Big Net" Ability affect its retreat cost?
Nope, if a Pokemon's Retreat Cost is set to zero by an effect such as Rescue Board, it cannot be increased by Big Net.
Source: Twilight Masquerade FAQ; TPCi Rules Team (2024-05-23)

Relevant cards

Note: All applicable cards may not be listed below.
SV6_5
SV6_5
SV5_159
SV5_159