There might be some confusion here. You can’t manipulate bones in object mode. There’s nothing you can do to a bone in object mode. If you think you are, what you’re probably doing is transforming an armature object.
Transforming an armature is a lot like transforming an imaginary uber-root bone. But not exactly. There are times when you want to transform an armature, because it creates the space that the armature transformations operate in, but it’s kind of unusual, kind of advanced. In general, you don’t want to be transforming armatures-- you want to be transforming the bones inside of them, in pose mode.
Origin of what? Of the bone? Enter pose mode, select bone, snap cursor to selection, enter object mode, set origin->origin to 3D cursor.
Of the armature? In object mode, select the armature, snap cursor to selection.
Of the object? Same basic process, works for me.
Do you want to send the pose of the bone to the 3D cursor, or do you want to set the rest position of the bone to the 3D cursor? That’s the difference between snapping it to cursor in pose mode and edit mode respectively. If the bone has any transformed location, snapping it to cursor in edit mode won’t mean that it’s at the cursor in pose: it will be at cursor, and then the transforms it has will take it off the cursor.
You want a bone for the pool stick, yes?
- Fix the pool stick’s origin. Snap cursor to some verts and set its origin to someplace appropriate.
- Unparent the pool stick with clear parent. Not sure if you need to, but follow it up with unparent with clear parent inverse.
- Clear all transforms on the pool stick.
- In edit mode, change the orientation of the bone to match the pool stick.
- Select the pool stick, shift select armature, enter pose mode, select bone, ctrl-p -> parent bone relative. (In your file, I don’t think it’s bone relative, but I suggest bone relative parenting.)
After that, never give the armature or the pool cue any transforms. There is one control for the pool stick, one way that you’ve set up to interact with it, and that is via the bone, in pose mode. If you want, go ahead and put transform locks on the object.
There are probably some interesting misconceptions worth getting cleared up behind that, but it’s hard to understand what you think is happening. Anything in Blender that has an origin, has one because it allows it to have transformations and a transformations space. An origin is the point that the bone or object rotates about or scales about. The orange dot is not the origin of a bone. It is the origin of an armature, which contains bones but is not a bone. The origin of a bone is the head of the bone (easier to see if you switch to octohedral view). If you move a bone, and then scale it, does it scale about the moved position of the head? It does. This is why bones have origins.