Using the code from this post you could move the plot to matplotlib and draw the colorbar with matplotlib:
from sympy import symbols
from sympy.plotting import plot3d
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
x, y = symbols('x y')
plot1 = plot3d(x*y, (x, -5, 5), (y, -5, 5), show=False)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
backend = plot1.backend(plot1)
backend.ax = ax
backend._process_series(backend.parent._series, ax, backend.parent)
plt.close(backend.fig)
ax.collections[0].set_cmap('inferno') # optionally change the colormap
plt.colorbar(ax.collections[0])
plt.show()
