You are correct that it is all radial: towards or away from the radar. Unfortunately, motion in other directions is not available. If you imagine motion of a target that is moving in a perfect circle whose center is the Bumblebee, no motion would be detected since there would be no change in offset between the signal and response.
As I read the Bumblebee tutorial, all the direction and speed are relative to the radar, the speed away from or close to radar, the direction is the angle between a target and the radar.
While what I want is the moving speed of the target, and its moving direction
Can I do that?
Yes you can. Read the Bumblebee tutorial on this site, especially sections 3 and 4. If you sample frequently enough relative to the target speed you can get both direction and speed. By calculating net cuts per second you can tell direction. By using the cut length you can tell speed.