|No, because the bridge mode will pass all the traffic from the internet directly to your internal computers.|
That also means, the the internal computer will have to authenticate to your ISP by itself and it'll get the public ip address. The routers firewall will also not work.
My suggestion is, let the router make the authentication and firewalling. The internal computers will get local ip addresses, e.g. 192.168.1.x and can access the internet through the router.
Read the manual for whether you have to make special settings in the router, to use file and printer sharing in the local network.