My M3 had intermittent steering shakes. My mechanic suspected front brake lines causing a hydraulic lock... Got the lines replaced. Still got the shakes. The mechanic suggested I check for a sticking caliper - after the shakes you stop and put your hand near (not on) the wheels to check for excessive heat. Sure enough the front right wheel/caliper was red hot.
I took it to my 'brake' guy to get the calipers serviced - he put in new seals and new pistons. All fixed. You cannot check the caliper piston without dismantling it.
If this is your problem you can either get the calipers replaced (BMW does not sell the pistons separately) or get a brake specialist to source a piston. There is a cost difference.