Even if whatever causes ME can be transmitted sexually, people need to be susceptible in order to develop ME. She could arrange for testing the genes that seem to be causing troubles with methylation/glutathione production, etc.
But generally, I wouldn't worry about her catching ME, especially since you aren't (presumably!) related. We're a very small portion of the population. Also, if you've been around each other a lot, snogging, etc, odds are she would have caught it from you already if she was going to. At least, I'm quite sure I didn't get it from having sex (or from snogging).