You cannot bridge to a WiFi client connection. That's why when you set up wireless bridging (WDS), you have to enable it on both ends. If you want to connect networks over a wireless link you must either configure WDS on both ends, use some form of NAT (sometimes called a "client bridge" but it actually NATs the MAC address), or use routing rather than bridging.
To preserve WiFi bandwidth (and for a few other historical reasons), the access point will only send non-broadcast traffic over the WiFi link if it's directed at one of its clients. Any machines connected to the virtual wireless interface are not clients of the access point connected to the real wireless interface. So the access point is not permitted to send packets bound for them over the real wireless link.
Sadly, WiFi is just enough like Ethernet to make people expect it to work the same way. But it is not wireless Ethernet. It's its own protocol with its own rules. WiFi-to-Wifi bridging is only supported with WDS on both ends.