Don't despair. Once my car had this same shudder going up thru a similar speed range. One thing I had was an after market wheel and I learned about Hub Centric Ringsmgot a set ,put them on and shudder gone....for a while then it was back. That was remedied after replacing the Thrust Arms with Bushings, yes arms and bushings not just the bushings. Driving it with the severe shudder must have damages the ball joint and torn the bushing which now that the forces weren't being released with the wheels revealed damage done before.
So now great new Thrust arms and bushings, Hub Centric Rings but i have a little vibration when braking.... New Rortos and pads. No problem but when i take it up the highway to Bed the pads and rotors... wtf? Wild shudder again... mystified was I untill I tried just swapping the rear tires to the front. Turns out the tires on the front had worn unevenly . Once newer tires were on the front the car again drove smoothly. Check your tires.If you have non stock rims they require hub centric rings though that would have been evident by now. A bad tie rod end,lose might also contribute. Good luck. It is possible to return your car to a condition where the ride is as it was meant to be.
1995 540i Manual build 1/95