How to run commands as in a queue

Problem

I need to do a lot of copying of various files to various folders. I can add all my copy commands to a bash script and then run that, but then I must wait until it finishes if I want to add more commands to that copying "queue". Is there a way I can run commands as a queue and sort of add more commands to that queue while things are running? Explained in a different way, I want to start a long running task. While that is running I want to start another one that does not actually start until the first one is done. And then add another after that last one and so on. Is this possible somehow?