I created my first sight at one physical location on a computer there. I am not at a different physical location on a different computer.
How do I access the “source” of my published site? Or do I need to handle that myself with something like Dropbox?
You export it to a location you set in the Settings of the project. Then upload them where you want them.
It might be helpful for you to read through the Docs and get some info on how things work in the app. 
Thank you for your quick and helpful reply.
As you say, “You export it to a location you set in the Settings of the project.”
So, my follow-up questions is, how do I get that information off of my other computer, now, when I have no access to it?
Which is kinda the reason that I posted my original question.
ahh ok I see where you’re going with this now lol.
Set up a folder on your current computer and export it there. It doesn’t sync with other computers that I’m aware of, just saves the files to your local computer that you’re on. I don’t believe there will be any way for you to get anything from the other computer at all other than copying the files from the old computer to the new one, but if you can’t get to themt … I hate to be the bearer of bad news, but it’s gone unless you can find a way to get it from the other computer … that’s what external drive backups are for 
So, as I postulated earlier, I need to put my project folder on Dropbox (or github) because there is no mothership that keeps track of my projects. No problem. Now I know.
I also need to wait until I get back on the other machine to deactivate the website I was using as a sandbox.
I copied the .bsdesign file from my remote computer to my local computer. When I attempt to open it I get an error. So I went back to my remote computer and did a save as to Dropbox. I attempt to open that file on my local computer and get the same error. Both of these files open fine on the remote computer.
I am uncertain how to solve this problem.
I was able to open the file after copying it from Dropbox to a local non-Dropbox folder.
Glad you got it all worked out, hope the rest goes better for you
I used to have this problem last year, its something to do with the way dropbox syncs the files, I found the work around was to pause sync on dropbox (right click the dropbox icon in the bottom right), just remember to turn it on again once you’ve finished.