Aha! Found the answer here:

cbar.ax.tick_params(labelsize=10) 

P.S. Upvote that answer and give Paul some love!

use cbar.ax.tick_params(labelsize=10)

From here and here

It is a matplotlib problem and not a GeoPandas problem.

See the solution of Seb Bacon: geopandas-legend-font-size.ipynb

As the Jupyter notebook has problems (error opening it), I describe it here.

The legend is actually a Colorbar object. To change the legend's font size, we have to get hold of the Colorbar's Axes object, and call .tick_params() on that.

import geopandas as gpd
world = gpd.read_file(gpd.datasets.get_path('naturalearth_lowres')) 
world = world[(world.pop_est>0) & (world.name!="Antarctica")] 
world['gdp_per_cap'] = world.gdp_md_est / world.pop_est

First, we call the .plot() method as usual, but we capture the return value which is the Axes of the map.

ax = world.plot(column='gdp_per_cap', cmap='OrRd', legend=True)

We can use this to get hold of the Figure that contains the Axes.

fig = ax.figure

The Figure has two Axes: one for the map, and one for the Colorbar. The one we care about is the second one.

cb_ax = fig.axes[1] 

We can now set the font size for the Colorbar. Other parameters for tick_params are documented at: matplotlib.axes.Axes.tick_params

cb_ax.tick_params(labelsize=10)

cb_ax.tick_params(labelsize=20)

I agree with francesco, but even shorten to one line:

plt.colorbar().set_label(label='a label',size=15,weight='bold')

You can change the tick size using:

font_size = 14 # Adjust as appropriate.
cb.ax.tick_params(labelsize=font_size)

See the docs for ax.tick_params here for more parameters that can be modified.

This two-liner can be used with any Text property (http://matplotlib.org/api/text_api.html#matplotlib.text.Text)

cb = plt.colorbar()
cb.set_label(label='a label',weight='bold')

or:

plt.colorbar().set_label(label='a label',size=15,weight='bold')

How about this:

...
fig, ax = plt.subplots()
cmapProp = {'drawedges': True, 'boundaries': np.linspace(0, 1, 13, endpoint=True).round(2)}
m = ax.imshow(data, cmap=plt.cm.get_cmap('Oranges'))
m.set_clim(0, 1)

# And here try this:
cbar = ax.figure.colorbar(m, ax=ax, **cmapProp)
cbar.ax.tick_params(labelsize=25)  # set your label size here
...

Out:

bold labels:

...
cbar = ax.figure.colorbar(m, ax=ax, **cmapProp)
cbar.ax.tick_params(labelsize=25)
for tick in cbar.ax.yaxis.get_major_ticks():
    tick.label2.set_fontweight('bold')
...

Out: