Hey Stani,
I'm not sure what programming language you are using, but VISA support events. Typically, all you have to do is setup your VISA resource, and then enable the VISA event you want to use. In your case the Characters at serial port event. Then wait on the event. After, the event occurs you just need to perform the VISA read. Attached is a LabVIEW example that illustrates this.
-JoshuaP