When you copy/paste text from MicroStation into another application such as Excel, Word or even Notepad, the text will be pasted in the same order it was drawn in the design file. If this isn't correct, you have to re-order your text using this workflow:

Using the selection tool select the text elements in the order you wish them to be pasted.
Then use the keyin WSET ADD;WSET DROP or....
ORDER ELEMENT FRONT or...
Select EDIT > BRING TO FRONT

This will rewrite the elements in the same order that the selection set was created.

With thanks to Rudi Wells for sharing this nifty trick!

UPDATE:  This does not work in MicroStation V8i.