I have travertine in my shower.... miles of it.
Be certain that you don't skimp on sealer. It wil be fine.

We install travertine every day and I personally have it in my shower. It is important to seal it with a good sealer and you will find that it will protect your material well. The more dense the travertine the better off you are. The porous tiles such as gold leave additional room for mold growth. Your supplier can show you the difference. Generally the more solid the color, the denser the material. Lastly, be sure when you clean the area that you don't use bleach as it will damage the stone. There are several products on the market recommended for cleaning travertine.

the Romans used travertine on buildings which still stand today! just make sure you seal, and re-seal as needed. use a squeegee after each shower. don't use any abrasive cleaning methods or acids to clean (citric cleaners, vinegar are acidic). travertine is a natural stone, and will absorb water if not properly sealed.