If you want a nice bullnose on your travertine tiles then you have a couple of options. You can have a tile shop add the curve for you on your tiles but this can be very expensive as the process is labor intensive. You can purchase travertine bullnose trim pieces which have been done in a factory setting so they are not as expensive but there is still a cost. The most economical method for the do-it-yourselfer is to add a travertine bullnose yourself.
This is really not as difficult as it may sound especially if you are familiar with grinding and sanding. Be sure to think about the safety equipment you will need first. Always wear safety glasses whenever you are doing any grinding or sanding as a piece in the eye can easily cause blindness. Also, a respirator is always a good idea when grinding stone as the dust can get into your lungs and cause problems down the road. Another safety matter is the speed of the grinder you use. Be sure to use a variable speed and never exceed about 3000 rpm as faster than this can cause parts of the sanding disk to fly off. A standard grinder turns at between 7500 and 8500 rpm so you can see that it is necessary to get a variable speed.
The best method for cutting the travertine bullnose is to do it in stages. You will be using sanding wheels of from 50 grit to about 400 grit. The finer grits are not needed until the later grinding stages. Determine the size of your bullnose and then place a line on the top and side of the tile that will mark the end of the curve. Go halfway back to the edge and place another line. This will mark the edge of your first 45 deg cut. Use a low grit pad and grind to these lines at a 45 deg angle. After this cut, split the difference again and grind this angle on both the top and the bottom. You can now split the difference again or just continue to sand by eye.
When the curve is close to what you desire the start using finer grind sanding disks. 80 grit will still remove material and so will 120 very slightly. Once you get to 240 your are mostly just taking out scratches and then 400 gives you a shine. Usually the 400 is used to complete the smoothing and then muriatic acid solution with water, 10% acid, is used to give it the honed look like the face. The bullnose is a very nice addition to the edge of travertine tiles.
These steps will answer how to bullnose travertine tiles. You can also use this method to create travertine trim pieces. Often times travertine bullnose trim is used on the edges of a worktop or countertop and then the center area is another tile. This works really well if the travertine trim is a different hue than the second type of tile which allows for a great contrast.