We had a 330i - it used hardly any oil. My cousin had one and it was going through a litre every 1000 miles - all within spec. Similar driving. Seems to afflict the M54B30...and not the others in the family to the same extent. My M52 2.8 with a 100k more miles on uses virtually no oil in comparison being driven in the same manner

It's a known feature with them. I believe, as on the M5 V8 engine, they modded the oil control rings partway through production - it may be down as well partly to how they were run in
If you do a search for 330 oil consumption on google you will find plenty of info.