Stopped my steering shudder.

Found a shop that knows how to balance rims. seems my BMW dealership can't do it. Anyway while in the air I spoted the cars got a cracked cover by the front right wheel and I used a long lever and found my lower control arms rear bush is shot probably from impact damage caused when i hit a tire some months back. How I know it was then is because it resulted in me needing to get an alignment. Anyway now i need to replace it. Question is can i replace just the bushing. My steering is tight and has zero play so I don't think i need to replace the arm just the bushing.

I will be doing both sides arms or just bushings no sense in being under the car twice..

Lee