Ffisegydd's answer works good, but if you are trying to increase the font size but some numbers disappear because of big size, you can do

cb = plt.colorbar()
for t in cb.ax.get_yticklabels():
     t.set_fontsize(20)

If you are here because you're trying to increase font size, but some numbers disappear because of big size with the above answer, you can do

cbar = plt.colorbar()
for t in cbar.ax.get_yticklabels():
     t.set_fontsize(20)

You can adjust size of major and minor ticks using this reference. https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.axes.Axes.tick_params.html You can change lenght and width = size. For example:

cbar.ax.tick_params(labelsize=40,length=10, width=4, which="major")

This makes labels of my colobar larger, and major ticks are longer and wider.

One option is to just format the ticklabels manually. There is probably a better way but this usually works for me.

cbar.ax.set_yticklabels(['{:.0f}'.format(x) for x in np.arange(cbar_min, cbar_max+cbar_step, cbar_step)], fontsize=16, weight='bold')

Edit:

If you don't want to figure out the ticks yourself you can use:

for l in cbar.ax.yaxis.get_ticklabels():
    l.set_weight("bold")
    l.set_fontsize(16)

You may need to call draw() if they are not properly updated. This can be reduced to a one liner with:

setp(cbar.ax.yaxis.get_ticklabels(), weight='bold', fontsize=16)

If I use @Yugi's answer, I will get latex errors. You can also set the fontsize with:

ticklabs = cbar.ax.get_yticklabels()
cbar.ax.set_yticklabels(ticklabs, fontsize=10)