I have bought several bags for this camera, but this one has proven to be the best for me:
Lowepro Dashpoint 10 Camera Case
Lowepro Dashpoint 10 camera case (camera case)

This bag can be used as a shoulder bag just as well as a belt bag.
However, there is one 'flaw' (which bothers me :
- No additional battery fits in the bag - only the camera itself
Otherwise TOP for me

Cullmann Malaga Compact 400
Cullmann Malaga Compact 400 (Camera shoulder bag, 0.40 l)

which fits perfectly for
- camera in the main compartment
- 2 suitable batteries in the slot in the main compartment on the back inside
- 1 cleaning cloth and a tripod plate in the zip pocket on the front

I have these and am completely satisfied. It can be worn directly on the shoulder or stowed in a messenger bag or rucksack Sony Lcs-Rxg (camera case, 0.82 l)

I ordered these to go with it:
Sony Lcs-Rxg (camera case, 0.82 l)
It's not cheap as it's made of leather, but it's well protected, can be hung around and, above all, the camera fits in well even with the optional grip handle. Other bags seem to have a problem with this.