Why I can still access modem GUI when it is bridged?

Solution 1:

Your first graphic properly depicts the modem in bridged mode. The second graphic does not correctly depict bridged mode. It's actually not a valid network scenario since a device cannot have the same IP address assigned to multiple interfaces.

When your ISP modem is not bridged it acts like a router (i.e. an OSI layer 3 device). The public IP address associated with your Internet connection is assigned to the modem's WAN interface. Further, its LAN interface will likely have a private IP address (e.g. 192.168.1.1). This means that if you connect your own router to the modem, its WAN interface misty be assigned an IP address on the same subnetwork as the modem's LAN interface, for example 192.168.1.2. Then your router's LAN interface would need to be configured to use a different subnetwork for its LAN interface, e.g. 192.168.10.1

When your ISP modem is bridged it stops acting as a Layer 3 device and instead simply forward all of the frames it receives between your router and the ISP's network*. As a result it doesn't have any IP address associated with it and you must use your own router (using your own router is optional if using the modem in non-bridged/router mode). The public IP address for your Internet connection is then assigned to the WAN interface of your router and you're free to use whatever IP address for its LAN interface.

I can't picture what happened during the bridged mode and how HostA can still access 192.168.1.1?

You don't say which device's configuration page you reach when you connect to 192.168.1.1, but I'm guessing it's your router's. If so that's actually expected behavior as explained by the above description of bridged mode.

*Even in bridged mode the modem will respond to a connection attempt to the management IP address configured on its LAN interface. This is necessary so you can still access it to change its configuration.