Mixed mode is only half the solution/problem. You really need to know what kind of session you burned - data or music/video (which are pretty much the only choices).
Your CD/DVD burning app also needs to be able to support "multi-session" which almost all of them can do. You then need to be able to tell if there are still more "sessions" available on your disk which most burner apps can detect. In other words, if you haven't "closed" your CD/DVD disk with regard to sessions then you should be able to squeeze a bit more data on it assuming there's room - and possibly assuming you're able to burn mixed mode CD/DVD's too (which we still don't know is even an option). You also need to be sure that whatever reads your CD/DVD can actually read a multi-session as well. Most can but some can't!
Multi session limitations is usually not a big deal with re-writeable disks. After all, you can totally erase a re-writeable CD/DVD and start all over should you happen to make a mistake or something. That's the beauty (and expense) of re-writeble disks. But once you close a regular CD/DVD then that's it. You're done. Period. No more data can be written no matter what. (It's a lot like punching out the write tabs on a cassette tape - assuming you know what that is.)
Therefore, I would advise getting a thumb drive since it's almost too simple to use. Or possibly upload your file to somewhere like Filedropper, Easyshare, Badongo, or even good old Drop Box so you can then download it whenever you get to the machine you intend to print from - and assuming that machine has Internet access. Either that or just buy another 50-cent CD/DVD and be sure to leave the sessions open for any future files to be burned.