How can I change legend bands and reflect those results on the mesh?

You need to define scalar_bar_args argument for the plotter.add_field method. This will change only legend properties. To sync it with mesh, use same values for n_colors and n_labels as direct argument for plotter.add_field.

import os
 
from ansys.dpf import core as dpf
from ansys.dpf.core.plotter import DpfPlotter
 
out_path = r"\PATH\TO\RST"
rst_path = os.path.join(out_path, "file.rst")
 
ds = dpf.DataSources(rst_path)
model = dpf.Model(ds)
mesh = model.metadata.meshed_region
 
nsn = ["B1", "B2"]
for ns in nsn:
    mesh_scoping = dpf.operators.scoping.on_named_selection(named_selection_name=ns,
                                                            data_sources=ds).outputs.mesh_scoping()
    mesh_region = dpf.operators.mesh.from_scoping(scoping=mesh_scoping, mesh=mesh).outputs.mesh()
    elastic_strain = dpf.operators.result.elastic_strain(data_sources=ds, requested_location="Nodal",
                                                         mesh_scoping=mesh_scoping)
    es_f = elastic_strain.outputs.fields_container()[0]
 
    plotter = DpfPlotter()
    sargs = dict(title="Legend", fmt="%.2e", title_font_size=30, label_font_size=20, n_labels=3, n_colors=2)
    plotter.add_field(es_f, meshed_region=mesh_region,
                      label_text_size=15,
                      label_point_size=5,
                      scalar_bar_args=sargs,
                      n_colors=2,
                      n_labels=3)
 
    plotter.show_figure()