Set the normal
The default values of cutting plane coordinate and normal are (0, 0, 0). A zero length normal is invalid and quite likely does nothing.
Test script
Here is a minimal working example of a script, adds a cube, runs the operator with plane coordinate at origin and its normal as the x axis. Recommend setting up a little script like below when asking questions
import bmesh
import bpy
from bpy import context
bpy.ops.mesh.primitive_cube_add()
ob = context.object
me = ob.data
bm = bmesh.new()
bm.from_mesh(me)
print('Nverts0',len(bm.verts), len([v for v in bm.verts if v.is_valid]))
bmesh.ops.bisect_plane(
bm,
geom=bm.edges,
dist=0.0001,
plane_co=(0, 0, 0),
plane_no=(1, 0, 0),
use_snap_center=False,
clear_outer=True,
clear_inner=False,
)
print('Nverts1',len(bm.verts), len([v for v in bm.verts if v.is_valid]))
bm.to_mesh(me)
Result
Nverts0 8 8
Nverts1 12 12
Effectively bisecting all x axis aligned edges, creating 4 ngons with 6 verts. Nothing to clear as faces are not "ripped".
Input geometry
For clear to work on a mesh that has faces, we are going to need to add the faces and verts to the geometry input of the operator. Recommend with geom
giving all geometry of a region of interest will make all options work as expected.
geom=bm.verts[:] + bm.edges[:] + bm.faces[:],
making this change an running again
Nverts0 8 8
Nverts1 8 8
Has bisected cube, same vert count one less face. The "outer" is cleared, ie all resultant geometry on the input normal's side of cutting plane.

Return Dictionary
Bmesh operators return information in a dictionary.
ret = bmesh.ops.foo.bar(blah)
in the case of bisect plane it has members "geom_cut" the edges and verts of the cut and "geom".
Some Examples of using bmesh bisect plane operator.
Python: Bisect mesh into n parts, without separate 'LOOSE'
using bisect but still failing
Slice up terrain mesh into chunks
How to get part of a mesh with Python API, which requires breaking down some faces?
Cutting a mesh in half
How to extract side-view outline (e.g. top view) of a 3D object to 2D surface?
Transform cylinder to flat plane - cylinder maze map