From what I can tell, Bridge should get the 2nd seed based on Premier League play.

The Challenge League rules say the following:

"a. Seeding for the SCSCL playoff will be based on each team’s league standings (Region III Premier League or SCSCL)
for game results completed when the SCYSA calendar date indicates that Challenge league play ends. The teams (two
maximum) playing in the Region III Premier League will be seeded one (1) or two (2) based on their winning percentage
against common opponents in the Region III Premier League and the first six (6) teams from the SCSCL will be seeded
three (3) through eight (8)."

A document on the SCYSA Website entitled "Challenge/Premier League Outline" states the following:

"If you are a SCYSA State Challenge Cup Winner or 2nd Place Winner, then you will be asked to play in the Region III
Premier League. If 1st or 2nd place decline the opportunity, then 3rd place will be asked. These teams must be comprised of the number of players listed in the chart below from the prior years 1st or 2nd place team. These two teams will be seeded 1st and 2nd in SCYSA State Challenge Cup based of their league record."

I can find no mention of the 2nd Premier team being seeded by Challenge League results rather than by Premier League participation.