I use 2x6 blocking screwed in between the studs. Its pretty standard as far as grab bar reinforcement. I do the same thing with the support for shower valves. I like 2x6 lumber for this as in my opinion it splits a lot less than the 2x4's. Framing lumber is very poor quality nowadays. Just make sure you don't put any framing where the shower arm will go besides the support for the elbow. I've had to reframe numerous showers because the stud was right in the center of the shower where the arm was going.
Its not a very good picture of it, but you can see how I put the grab bar blocking in my basement bathroom. I also put it in where the towel bars will go. It makes for a much better installation there too.