What could be triggering this on my end?
Using the information provided in the post, my best guess would be they have a faster internet upload speed. They can upload the files fast and the script running on the server does not timeout. When you do (again, just a hunch), your upload speed is low, so it takes a longer time to upload the files and the script times out.
You could test this at a friends or other location that you can confirm has faster upload speeds (which seems the case already).
You can test your upload speed here:
http://www.speedtest.net/
That said, if you have a too busy router (other users hogging bandwidth), or yourself have net connected processes doing the same, this can also affect you upload speeds. A poor connection, improper browser settings, malware, can all also contribute to this.
That could very well be it, as the connection I’m currently using is sub-par. I have however uploaded a couple hundred files over the last couple weeks without this issue. Seems to have just sprung up.
I have changed where my wordpress blog is being hosted since then though. I was on a standard shared plan, and am now on a dedicated. That might have something to do with it?
if you were previously on shared and now you are on dedicated…. that is a good thing and only helps your plight. My best guess would be server side php.ini upload limits or the max file time. Talk to your host and figure out the max limits you can set in your php.ini file and then refresh or clear your cache and try again.
Also, if you are uploading images only try this: https://wordpress.org/plugins/wp-smushit/
If not, give this a read: http://premium.wpmudev.org/blog/bulk-upload-files-to-wordpress-media-library-using-ftp/?utm_expid=3606929-34.mZctMukzSv6Wvz3lKaD43w.0&utm_referrer=https%3A%2F%2Fwww.google.com%2F