If you would rather rely on the main PyShp version, simply copy and paste the conversion function in the code below to your own script and call on it to convert any of your shapely geometries to a pyshp compatible shape. To save them you then simply append each resulting pyshp shape to the shapefile.Writer instance's ._shapes list (for an example see the test script at the bottom of this post).

Note however: the function below will NOT handle any interior polygon holes if there are any, it simply ignores them. It is certainly possible to add that functionality to the function but I have simply not bothered yet. Suggestions or edits to improve the function are welcome :)

# THIS FUNCTION CONVERTS A GEOJSON GEOMETRY DICTIONARY TO A PYSHP SHAPE OBJECT
def shapely_to_pyshp(shapelygeom):
    # first convert shapely to geojson
    geoj = shapely.geometry.mapping(shapelygeom)
    # create empty pyshp shape
    record = shapefile._Shape()
    # set shapetype
    if geoj["type"] == "Null":
        pyshptype = 0
    elif geoj["type"] == "Point":
        pyshptype = 1
    elif geoj["type"] == "LineString":
        pyshptype = 3
    elif geoj["type"] == "Polygon":
        pyshptype = 5
    elif geoj["type"] == "MultiPoint":
        pyshptype = 8
    elif geoj["type"] == "MultiLineString":
        pyshptype = 3
    elif geoj["type"] == "MultiPolygon":
        pyshptype = 5
    record.shapeType = pyshptype
    # set points and parts
    if geoj["type"] == "Point":
        record.points = geoj["coordinates"]
        record.parts = [0]
    elif geoj["type"] in ("MultiPoint","Linestring"):
        record.points = geoj["coordinates"]
        record.parts = [0]
    elif geoj["type"] in ("Polygon"):
        record.points = geoj["coordinates"][0]
        record.parts = [0]
    elif geoj["type"] in ("MultiPolygon","MultiLineString"):
        index = 0
        points = []
        parts = []
        for eachmulti in geoj["coordinates"]:
            points.extend(eachmulti[0])
            parts.append(index)
            index += len(eachmulti[0])
        record.points = points
        record.parts = parts
    return record

Here is a full standalone test script:

### HOW TO SAVE SHAPEFILE FROM SHAPELY GEOMETRY USING PYSHP

# IMPORT STUFF
import shapefile
import shapely, shapely.geometry

# CREATE YOUR SHAPELY TEST INPUT
TEST_SHAPELYSHAPE = shapely.geometry.Polygon([(133,822),(422,644),(223,445),(921,154)])

#########################################################
################## END OF USER INPUT ####################
#########################################################

# DEFINE/COPY-PASTE THE SHAPELY-PYSHP CONVERSION FUNCTION
def shapely_to_pyshp(shapelygeom):
    # first convert shapely to geojson
    geoj = shapely.geometry.mapping(shapelygeom)
    # create empty pyshp shape
    record = shapefile._Shape()
    # set shapetype
    if geoj["type"] == "Null":
        pyshptype = 0
    elif geoj["type"] == "Point":
        pyshptype = 1
    elif geoj["type"] == "LineString":
        pyshptype = 3
    elif geoj["type"] == "Polygon":
        pyshptype = 5
    elif geoj["type"] == "MultiPoint":
        pyshptype = 8
    elif geoj["type"] == "MultiLineString":
        pyshptype = 3
    elif geoj["type"] == "MultiPolygon":
        pyshptype = 5
    record.shapeType = pyshptype
    # set points and parts
    if geoj["type"] == "Point":
        record.points = geoj["coordinates"]
        record.parts = [0]
    elif geoj["type"] in ("MultiPoint","Linestring"):
        record.points = geoj["coordinates"]
        record.parts = [0]
    elif geoj["type"] in ("Polygon"):
        record.points = geoj["coordinates"][0]
        record.parts = [0]
    elif geoj["type"] in ("MultiPolygon","MultiLineString"):
        index = 0
        points = []
        parts = []
        for eachmulti in geoj["coordinates"]:
            points.extend(eachmulti[0])
            parts.append(index)
            index += len(eachmulti[0])
        record.points = points
        record.parts = parts
    return record

# WRITE TO SHAPEFILE USING PYSHP
shapewriter = shapefile.Writer()
shapewriter.field("field1")
# step1: convert shapely to pyshp using the function above
converted_shape = shapely_to_pyshp(TEST_SHAPELYSHAPE)
# step3: tell the writer to add the converted shape
shapewriter._shapes.append(converted_shape)
# add a list of attributes to go along with the shape
shapewriter.record(["empty record"])
# save it
shapewriter.save("test_shapelytopyshp.shp")

If you would rather rely on the main PyShp version, I have also provided a conversion function below:

# THIS FUNCTION CONVERTS A GEOJSON GEOMETRY DICTIONARY TO A PYSHP SHAPE OBJECT
def shapely_to_pyshp(shapelygeom):
    # first convert shapely to geojson
    try:
        shapelytogeojson = shapely.geometry.mapping
    except:
        import shapely.geometry
        shapelytogeojson = shapely.geometry.mapping
    geoj = shapelytogeojson(shapelygeom)
    # create empty pyshp shape
    record = shapefile._Shape()
    # set shapetype
    if geoj["type"] == "Null":
        pyshptype = 0
    elif geoj["type"] == "Point":
        pyshptype = 1
    elif geoj["type"] == "LineString":
        pyshptype = 3
    elif geoj["type"] == "Polygon":
        pyshptype = 5
    elif geoj["type"] == "MultiPoint":
        pyshptype = 8
    elif geoj["type"] == "MultiLineString":
        pyshptype = 3
    elif geoj["type"] == "MultiPolygon":
        pyshptype = 5
    record.shapeType = pyshptype
    # set points and parts
    if geoj["type"] == "Point":
        record.points = geoj["coordinates"]
        record.parts = [0]
    elif geoj["type"] in ("MultiPoint","Linestring"):
        record.points = geoj["coordinates"]
        record.parts = [0]
    elif geoj["type"] in ("Polygon"):
        record.points = geoj["coordinates"][0]
        record.parts = [0]
    elif geoj["type"] in ("MultiPolygon","MultiLineString"):
        index = 0
        points = []
        parts = []
        for eachmulti in geoj["coordinates"]:
            points.extend(eachmulti[0])
            parts.append(index)
            index += len(eachmulti[0])
        record.points = points
        record.parts = parts
    return record

Simply copy and paste the function to your own script and call on it to convert any of your shapely geometries to a pyshp compatible shape. To save them you then simply append each resulting pyshp shape to the shapefile.Writer instance's ._shapes list (for an example see the test script at the bottom of this post).

Note however: the function will NOT handle any interior polygon holes if there are any, it simply ignores them. It is certainly possible to add that functionality to the function but I have simply not bothered yet. Suggestions or edits to improve the function are welcome :)

Here is a full standalone test script:

### HOW TO SAVE SHAPEFILE FROM SHAPELY GEOMETRY USING PYSHP

# IMPORT STUFF
import shapefile
import shapely, shapely.geometry

# CREATE YOUR SHAPELY TEST INPUT
TEST_SHAPELYSHAPE = shapely.geometry.Polygon([(133,822),(422,644),(223,445),(921,154)])

#########################################################
################## END OF USER INPUT ####################
#########################################################

# DEFINE/COPY-PASTE THE SHAPELY-PYSHP CONVERSION FUNCTION
def shapely_to_pyshp(shapelygeom):
    # first convert shapely to geojson
    try:
        shapelytogeojson = shapely.geometry.mapping
    except:
        import shapely.geometry
        shapelytogeojson = shapely.geometry.mapping
    geoj = shapelytogeojson(shapelygeom)
    # create empty pyshp shape
    record = shapefile._Shape()
    # set shapetype
    if geoj["type"] == "Null":
        pyshptype = 0
    elif geoj["type"] == "Point":
        pyshptype = 1
    elif geoj["type"] == "LineString":
        pyshptype = 3
    elif geoj["type"] == "Polygon":
        pyshptype = 5
    elif geoj["type"] == "MultiPoint":
        pyshptype = 8
    elif geoj["type"] == "MultiLineString":
        pyshptype = 3
    elif geoj["type"] == "MultiPolygon":
        pyshptype = 5
    record.shapeType = pyshptype
    # set points and parts
    if geoj["type"] == "Point":
        record.points = geoj["coordinates"]
        record.parts = [0]
    elif geoj["type"] in ("MultiPoint","Linestring"):
        record.points = geoj["coordinates"]
        record.parts = [0]
    elif geoj["type"] in ("Polygon"):
        record.points = geoj["coordinates"][0]
        record.parts = [0]
    elif geoj["type"] in ("MultiPolygon","MultiLineString"):
        index = 0
        points = []
        parts = []
        for eachmulti in geoj["coordinates"]:
            points.extend(eachmulti[0])
            parts.append(index)
            index += len(eachmulti[0])
        record.points = points
        record.parts = parts
    return record

# WRITE TO SHAPEFILE USING PYSHP
shapewriter = shapefile.Writer()
shapewriter.field("field1")
# step1: convert shapely to pyshp using the function above
converted_shape = shapely_to_pyshp(TEST_SHAPELYSHAPE)
# step2: tell the writer to add the converted shape
shapewriter._shapes.append(converted_shape)
# add a list of attributes to go along with the shape
shapewriter.record(["empty record"])
# save it
shapewriter.save("test_shapelytopyshp.shp")