It is surprising that a client-bridge does not work. The problem I suspect is there are multiple modes these devices can run in. I do not know the details of that engenius device. The simple client bridge lets a single device hook up via ethernet. This really is not much different than a USB wifi nic it just uses a different type of cable....and of course all the configuration is done in bridge rather than the pc.
The problem comes if you want to run multiple devices behind the bridge. This is commonly done with a feature called WDS but many public wifi points have this disabled both for security reasons and because it allows them to control the number of devices/mac address that connect.
Some bridges can run in a...