That's a problem for the bridge device to sort out, not the hardwired ethernet gear that it connects.

Pre-made wireless bridges generally have web interfaces (and/or dreadful phone apps) to get them set up and chatting the right way.

It's a process that's very similar to that of configuring a home network router, except the bridge works in the opposite direction.

In this way, the devices with ethernet jacks have no idea what things like WEP, WPA, or wifi even are. And that's kind of the whole point. :)