So if you turn off bridge mode on the ISP router it works? Maybe check the IP and so on that the ISP router gets assigned then.
As a shot in the dark: maybe the fixed IP gets assigned according to the MAC address of the ISP router, in which case you might have to spoof the same MAC on your Asus router.
Another thing might be the ethernet port on the ISP router. I have one that allows bridge mode only on one specific LAN port.