virtualbox.org

The guest will not communicate when the host is using wireless. It works fine if the host is using the wired network.
I am using Virtualbox version 5.2.8 R121009 and have tired this on a couple of different versions on a couple of different computers.
The host is running W7 x64.
The guest is running W7 x32. The network adapter is set to Bridged.
It doesn't work with the cable connected checked or not.

Bridged over wireless don't always play nice. Bridged networking is outside the WLAN specification. Bridging to wireless is not really bridging. The guest shares the MAC of the host and the host does a sort of MAC-NAT translation based on IP addresses. Promiscuous mode doesn't exist in the official WLAN specifications.

It may or may not work. There's nothing you can do about it, sort of changing your hardware (95%).

Some combinations of Routers/Access Points, WLAN cards and drivers work, some don't. See: Bridging & Wifi - Supported hardware and add your experience.