If you actually bridged your USB/Ethernet adapter with your other adapter on your computer and got your mining setup to actually work you are NOT hiding your Antminer's IP address from your local network.

Instead of a bridge the correct way to do this would be to setup some kind of routing/NAT software on your computer and create a new subnet between your computer and Antminer. I've done this before at work (not for mining) when I had to hide a cluster of rogue, non-compliant, development servers from corporate IT .