It does get quite busy there, it was this week when I was last there, but you should find space somewhere.
West of Br 58 isn't the greatest as it suffers from the sloping side typical of the shortened sections of the Oxford, so you will be away from the edge. Also the retail park that TDH mentions is closing down for redevelopment so the car park may be inaccessible, but of it is still open the access point is close to the bridge by the winding hole..
East of 58 you have either the park moorings on the offside (north) which are 24h and popular, but easy access from the car park. Or the towpath which you can get to down a ramp from the bridge (personally I wouldn't stop my car on the bridge), from the top corner of tesco's car park, or maybe from the new houses roughly opposite where the park car park is.
Another option is the offside east of Br 59, it's a good edge and I did notice that there is at least one mooring ring last time I passed. Often see boats moored there and just a few steps from Crow Thorns.
image by andy3196, on Flickr