I believe it's made of ABS plastic, so yes it's difficult but not impossible.
First off you need to scuff all the plastic surfaces with Ajax and a red or grey scotchbrite pad. The ajax helps remove surface oils from the plastic. I would use the grey if you are not an experieced painter the red tends to leave scratches if you are not careful.
Then you need to use SEM (Brand ) Plastic prep solution. Followed by 2 coats of SEM Flexible bonding clear.
You should also use a flexible primer for ABS (Not Urethane ) Dupont makes a fantastic spray bomb for this.
Then you can follow with a Basecoat/Clearcoat system of choice. I prefere Dupont chromobase and then Chromoclear over the top. And that should cost you about
$100-$150 for materials. I painted my own from M3 bumper, but I do paint alot and do custom helmets and occasionally bikes.
Or you can leave it Black which I prefere also.
98 328is Sport Package M3-Spoiler and Front End,
Turner Motorsports 4 Wheel drilled Rotors.
Axxis Brake Pads, Teflon/Stainless Brake Hoses.
UUC Sachs Stage 4 Suspension.
Sway Bavarian Sway Bars.
H&H MotorSports Front and Rear Strut braces.
Conforti CAI and Shark Injector.
UUC System U DTM Exhaust
UUC Short shifter , Tranny Mounts and Clutch Stop.
F1Danza Lightweight Flywheel with M-3 Heavy duty clutch.
Factory BMW M3 Front Bumper with Splitter.
More to follow...MUCH MORE !