Bhabha scattering was one of the first scattering processes ever calculated. The reference is:
H. J. Bhabha, "The Scattering of Positrons by Electrons with Exchange on Dirac's Theory of the Positron", Proc. Roy. Soc. A154 (1936) 195.
For a view on few pages of the article, click here: p.195, p.202, p.206.

We are calculating quantum corrections to Bhabha scattering in QED and also in the electroweak Standard Model.
For a precise prediction of the small angle Bhabha cross section at a future linear collider, one has to calculate the electroweak corrections to 1-loop order and the QED corrections to 2-loop order.
The status of the projects is described in recent talks given at

       LL04 , DESY Workshop "Loops and Legs in Quantum Field Theory", Zinnowitz, Germany, 25-30 April 2004
       LCWS04 , "International Conference on Linear Colliders", 19-23 April 2004, Paris, France.