@Cory - Yes, only one needs to be wired to your ethernet. The others will link to it with wireless assuming they are within range. This is why they don’t sell many bridges (and why the bridges are often given away as part of a deal). I believe all the Sonos units have this capability (but you should probably confirm that be checking the product literature) - not 100% sure about the Play1 as I don’t have any of them (yet).
@Greg - The bridge is a Sonos-wireless-to-wired-ethernet bridge. So in my basement it is wired to my house ethernet and the other Sonos units in the basement connect to it with Sonos wireless. The bridge would not be connected by wire to the Sonos speaker.
I use the term Sonos-wireless because, while Sonos speakers use Wifi Frequencies, they are not interoperable with other Wifi devices. Also, Sonos specifies that you need at least one unit with a wired connected to serve as the gateway to the internet (via your home router). I assume this was due to concerns over bandwidth and latency if you tried to link it up with WiFi.