In reply to andy:
Traffic seems to flow both ways, i lived for 18 years between both of those locations, Acocks Green (On the train route between the 2!)
a good way would be as you said A41, ok it is an A road, but it is a Bus route too and has the odd stretch of Bus lanes, not much mind! it is worth having a look on Google street view and looking at some of the junctions, some are 'interesting.'
I still drive stretches of that route regularly and often see mad cyclists on it, but if needs be you can always Train part of it and cycle the rest as it follows the train line most of the way.
Post edited at 09:23