Airport Express (2007 vintage)
Sorry, confused. A 2007 vintage AirPort Express would have only one Ethernet port on the device. So, either you have a 2012 or newer version of the AirPort Express, or you may have meant to say that you have an AirPort Extreme.
If you do have an Airport Extreme, is this the "flat or square" version, or is this the older "round or dome" version of the Airport?
The Arris sends out a wireless signal which is unneeded and not wanted, because my Airport express sends the internet wi-fi signals to our home, and by an ethernet cable to my desktop. I understand I can call Comcast and ask them to turn off my wif-fi and change my Arris router/modem settings to the "bridge mode"
This sounds as if you may be confused about what "bridge mode" might imply.
Simply turning off the wireless function of the Comcast modem/router will do just that....turn off the wireless function. Nothing else will change, and the AirPort Express or Extreme will continue to operate exactly the same way that it does now.
This would be by far the simplest way to accomplish your goal.
If for some reason, you wanted to completely change the Arris modem/router to operate only as a modem......now "Bridge Mode" will come into play. It may or may not even be possible to configure the Arris device this way. That would be a question for Comcast support.
If it is possible, then the AirPort will need to be completely reset back to factory default settings and then set up again to work with your "modem".
So, with "bridge mode' on the Arris device, you will be looking at major changes to both the Arris and AirPort devices. There is really no advantage to doing things this way, and with major changes to two different devices, you will likely be calling the support folks for both Comcast and Apple, and having each blame the other for your problems.
In this regard, sometimes that fact that you might be able to do something does not really mean to imply that it would be a good thing to do.
My recommendation would be to simply ask Comcast to turn off the wireless function of your Arris modem/router and leave it at that.
But, it's your call.