I want my "pole" follow point B from point A with no stretching, this way
Intead of this I get this:
I'm not sure that's what you want because it's not clear to me but I give a try with this:
Create Bone1 and his child Bone2. Create Bone3 and his child Bone4. Give Bone2 an IK Constraint with Bone4 as Target. Now Bone2 sticks to Bone4.
For the rotation of Bone3: In the 3D View right panel (displayed with N), choose XYZ Euler instead of Quaternion. Create a keyframe at angle 0°, rotate the bone 180° and create a second keyframe, then in the Dopesheet press T > Linear and shiftE Linear Extrapolation to make the rotation perpetual.