Commonly there are 2 reasons why you get the "busy" message that won't let you unmount.
1) You are still somewhere in the mounted file tree (some terminal or program)
2) There is still data in the write cache that has not been written
Solution to one was posted above
For 2) do
It should write the remaining data in the write buffer.
This can take a while, wait until the prompt appears again.
Then try to unmount it.