This fundamental study of single bubbles rising in confined geometries was motivated by the aeration in membrane bioreactors. The parameters channel depth, bubble size, superimposed liquid velocity and rheology of the liquid (Newtonian, non-Newtonian) were varied. The flow field close to the bubble with a negative wake in the non-Newtonian liquid is discussed and a data presentation is introduced allowing a statistical analysis. Cumulative distribution functions for the velocity magnitude, vorticity, strain and shear stress are extracted from the flow fields for each parameter combination. Except for channel depth, almost all analyzed properties increased with increasing bubble size and superimposed liquid velocity. An influence of the rheology on the results is visible especially for the shear stress.