I found very little information online for curving a tile transition strip. They come in 8 ft. straight pieces at Lowe's and Home Depot. Fortunately, my brother-in-law curved the tile in his kitchen so we were able to copy his technique. He has hardwood on the other side of the tile, so he used a slightly different strip.
Our strip looks like this:
The idea is to create curves like this:
You can purchase flexible transitions online, but they are more expensive and have shipping costs. An 8 ft. piece at Lowe's is around $10.
First we marked the rectangle of where we wanted the tile to stop. Then we used a string attached to a carpenter's pencil to draw a radius on the corner we wanted to curve. You can't see it in the below photo because the strip is covering it, but you can see the corner.
We had a professional install our tile. He was able to complete the install easily. You will need to snip the aluminum boxes where the tile goes, as pictured below. I've highlighted the line on the floor where our curve is (click image to enlarge detail). Bend the strip as you go. Screw support blocks in the floor as needed to secure curve. Remove them after tile has completely set.
Depending on the curve, you may need to snip a little of the aluminum or a lot. As you can see, the cuts are wider on the bigger part of the curve and narrower when it starts to straighten out.
Click on image to enlarge detail.