debug_append.py

from bokeh.models.widgets import Button, Dropdown
from bokeh.layouts import column, widgetbox, row
from bokeh.io import show, curdoc, output_notebook
from bokeh.application.handlers import FunctionHandler
from bokeh.application import Application

def modify_doc(doc):

    # This works with Bokeh server and jupyter:
    main_button = Button(label='Refresh')

    # This only works in Bokeh server:
    # main_button = Dropdown(label='Refresh', menu=[('A', 'A'), ('B', 'B')])

    layout = column([main_button], height=200)

    def create_button(label):
        return Button(label=str(label))

    # Update the plot
    def update(*args):
        layout.children = layout.children + [create_button(len(layout.children))]

    main_button.on_click(update)

    doc.add_root(layout)
    doc.title = "Example"

run_mode = 'bokeh_server'
if run_mode == 'bokeh_server':

    # bokeh server:
    modify_doc(curdoc())

elif run_mode == 'jupyter_notebook':

    # jupyter notebook cell:
    output_notebook()
    handler = FunctionHandler(modify_doc)
    app = Application(handler)
    doc = app.create_document()
    show(app, notebook_url="localhost:8888")
    
else:
    raise NotImplementedError

Works in Chrome 58

Still Does not work on a fully up-to-date Firefox 54