From the matplotlib docs on scatter 1:
cmap is only used if c is an array of floats
So colorlist needs to be a list of floats rather than a list of tuples as you have it now.
plt.colorbar() wants a mappable object, like the CircleCollection that plt.scatter() returns.
vmin and vmax can then control the limits of your colorbar. Things outside vmin/vmax get the colors of the endpoints.
How does this work for you?
import matplotlib.pyplot as plt
cm = plt.cm.get_cmap('RdYlBu')
xy = range(20)
z = xy
sc = plt.scatter(xy, xy, c=z, vmin=0, vmax=20, s=35, cmap=cm)
plt.colorbar(sc)
plt.show()
