My 335i had same symptoms on cold start. If I drove off immediately, no problems, and car smoothens out after it warms up. However, I also was blowing black smoke out of tail pipes on WOT.
Did walnut shell blasting, and replaced all 6 spark plugs. Found plugs 1 to 3 were fouled (black w/ fuel smell). Afterwards, black smoke on WOT is now gone, but cold start issue is still there.
Pretty sure it's my bank 1 injectors. I had those injectors replaced under warranty, but bank 2 is still the original. Go figure.
PROcede | AMS FMIC | AR Catless DPs | AR Oil Cooler | BMS DCI
Wavetrac LSD | KW V3 w/ Swift Springs | M3 Front Suspension