Do it all the time, most instruments (all the good brands) have VISA controls. With this on most instruments you can script most user actions (like pressing buttons) and also do other things like data acquisition. The interface is independent of comm (USB, RS232, GPIB or Ethernet). First you need to establish communications and once you start sending commands you can do whatever the commands will allow.
Once I wanted to test USB faults and I didn't have a diff probe. The only way for me to get a differential measurement with an eye diagram was to do the subtraction on a PC (in fact a rep told me that they intentionally leave eye diagrams off of low speed scopes to force people to upgrade). So I wrote a script that would set up the instrument, detect a trigger and then download the data so it could be subtracted. I then checked the 'eye diagram' against the USB standards.
Usually an instrument will come with software to issue commands, which is invaluable because it can be difficult to establish communications (especially with RS232 with all the baud rates or ethernet with IPs). Most instruments have a separate VISA command manual and those can be hard to find sometimes on a website.
You can then use just about computer language to issue the commands, I favor RS232 because every language has (usually built in) ways to talk to a uart. One of the problems can be CR and LF and figuring out how the instrument gets its commands.
Some instruments have VISA .dlls/API's and those can be harder to work with.