You do have one intrinsic problem, your wall studs will be about 15 inches apart. to be precise, the studs will be 16 inches apart center to center of the next one. So, you will be able to anchor one (1) end of the bar to a stud the other will be molly bolts.
Now, you will need a very sensitive stud finder to locate one stud. You can get one for about $20, but I do not know if that quality of finder will go through the tile. The one I have will indeed, but its about $50. You do not want to spend this amount for one find.
Or you could just forget the location of any studs and drill open the tile and use molly bolts all the way around.
Here is what I would do; have your Mother enter the stall and find the appropriate location for the bar to be. Mark this area.
Now, with the end plates with the holes for mounting; place them in the area where you want the bar. with someone else holding the bar, place masking tape on the area where the brackets will go, mark with a pencil the holes in the mounting bracket onto the masking tape which is on the tile. Do this on both ends.
*** also, its very important that the brackets be as close to the center of each tile and NOT near the grout or the ends of the tile. The tile is stronger in the center of the tile and the ends and grout will surely split and crack. Remember, measure twice and drill once.
Now, tools for this job; a power drill preferably a 3/8 inch drill (common drill), two special spade drill bits for ceramic tile, and the amount of bolts for the project.
Consult a professional at your home center what you are doing and match the tile drill bit to the molly insert so that the hole is not too big or too small. It has to be just right, said one bear.
Now, starting each hole with the special tile spade bit requires steady hand and not too much drill speed. Place the point of the tile bit point on the mark on the tape and carefully apply small revolution pressure of the drill slowly making a small hole and making a good pilot point. This intial stage of tile drilling is important because if you apply to much speed the drill bit will "walk" all over the tile and score it. You want that bit to stay in its hole. Once you get going add some speed and you will soon go through.
do all holes the same way and then insert all the brackets and molly's and then secure them down tightly. You should be OK.
Now if all this seems intimidating and too much, then call a handyman for this project. I would do this for about $50 in labor. So, if you hire someone you can tell them how you want it done and where.