You could get a large USB stick, then make the backup software's bootable media, on the USB stick.
Then run the backup software from within Windows or from the USB stick, and STORE the backup on that same USB stick.
Then you would end up with the backup software (bootable) and the backup, on the same USB stick.
You could then put the USB stick in any computer and boot to the backup software that's on the USB stick, and just restore the backup that's also stored on that USB stick to whatever computer you... stuck that stick in.
You could also do the same with a small USB stick and an External drive (to store the backup(s))... I think.