Assuming I'm not misinterpreting the card, I think I can help illustrate how people are overthinking Wayfarer's Cost clause:
Imagine a card with bottom text which reads "this costs $2". You play a Bridge, and for an infinitesimal moment, the card would cost $1, but then you look at the card, and it says "No, I cost $2, remember?" Cost reductions may try to affect the card, but since its effect is persistent (doesn't matter if it's in play or not), it will always instantly reset itself to $2.
The difference between that card and WF? Well, sometimes WF says it costs $2, sometimes it says it costs $3, sometimes it says it costs $8, but whatever the case is, it always* explicitly says that it costs something. If it's telling you "I cost as much as that Estate you gained earlier", the Estate could be impacted by Bridges, but WF itself cannot, because every time you try to change its cost, it politely declines, "No, good sir, I keep telling you, I cost what that Estate you gained earlier cost".
In essence, one of the effects is going to have to fail since they're in conflict. Either Bridge tries to lower WF's cost, but can't, or WF tries to cost what the last gained card cost, but can't. The reason the former is more intuitive to me is because while both cards are trying to mess with WF's cost, bridge is doing so less precisely (it doesn't care what the card will actually cost, so long as it's non-negative), whereas WF has a precise number it's telling you it should cost, even if that number will change as your most recently gained card changes. At any point in time, WF has one specific number in mind.
*There is still the scenario where no cards have been gained this turn (or only Wayfarers have been), in which case I see no reason why Bridge couldn't reduce WF's cost. If no cards have been gained, WF's cost-locking effect isn't activated yet.