I'd like to create a FunctionSpace that is composed of $P_2$ (with degrees of freedom associated with the nodes and edge midpoints) and $B$ (bubble elements, degrees of freedom associated with the cell center of gravity).
FunctionSpace
Is this currently possible in FEniCS?
Yes, it it possible:
P2 = VectorFunctionSpace(mesh, "Lagrange", 2) B = VectorFunctionSpace(mesh, "Bubble", 3) V = P1 + B
Take look at the demo in dolfin/demo/undocumented/stokes-mini.
dolfin/demo/undocumented/stokes-mini