It is in fact the school BridgeTEFL is using for the CELTA. I registered for the CELTA through them and then went through the interview process with IH Budapest. And Bridge also confirmed prior to the interview that this is the school (their "partner") that they use in Budapest.
You can see some of what I have been thinking on my thread--Hamline or CELTA
--which is in this forum. Most people are telling me to do the CELTA; certainly everybody on this board.
Why did you choose to go through Bridge? Was it because of their job placement guarantee?