The problem is that while the FormatStrFormatter allows to set the format precisely, it is not capable of handling offsets like the 1e-7 in the case from the question.

On the other hand the default ScalarFormatter automatically selects its own format, without letting the user change it. While this is mostly desireable, in this case, we want to specify the format ourself.

A solution is to subclass the ScalarFormatter and reimplement its ._set_format() method, similar to this answer.

Note that you would want "%.2f" instead of "%.2g" to always show 2 digits after the decimal point.

import numpy as np; np.random.seed(0)
import matplotlib.pyplot as plt
import matplotlib.ticker

class FormatScalarFormatter(matplotlib.ticker.ScalarFormatter):
    def __init__(self, fformat="%1.1f", offset=True, mathText=True):
        self.fformat = fformat
        matplotlib.ticker.ScalarFormatter.__init__(self,useOffset=offset,
                                                        useMathText=mathText)
    def _set_format(self, vmin, vmax):
        self.format = self.fformat
        if self._useMathText:
            self.format = '' % matplotlib.ticker._mathdefault(self.format)

z = (np.random.random((10,10))*0.35+0.735)*1.e-7

fig, ax = plt.subplots()
plot = ax.contourf(z, levels=np.linspace(0.735e-7,1.145e-7,10))

fmt = FormatScalarFormatter("%.2f")

cbar = fig.colorbar(plot,format=fmt)

plt.show()

It's hard to test, since your example isn't directly runnable, but you should just be able to set the labels to whatever string you like. Something like so:

bound_labels = [str(v) if v <=1 else str(int(v)) for v in bounds]
cbar.set_ticklabels(bound_labels)

You can specify the format of the colorbar ticks as follows:

pl.colorbar(myplot, format='%.0e')

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)

A working example (for any value range) with five ticks along the bar is:

m0=int(np.floor(field.min()))            # colorbar min value
m4=int(np.ceil(field.max()))             # colorbar max value
m1=int(1*(m4-m0)/4.0 + m0)               # colorbar mid value 1
m2=int(2*(m4-m0)/4.0 + m0)               # colorbar mid value 2
m3=int(3*(m4-m0)/4.0 + m0)               # colorbar mid value 3
cbar.set_ticks([m0,m1,m2,m3,m4])
cbar.set_ticklabels([m0,m1,m2,m3,m4])