Here's the tape I used, in both 7/8" and 1/2" widths. Worked great. Circumferential tape around the splitter edge, with only the one existing screw in the bumper.
2011.5 E90 Dinan M3, SS II, M-DCT, EDC, M Drive. Winter setup 220M w/ 255/275 Blizzaks
Performance Mods: Dinan St.1 suspension, exhaust, intake; TTPs; BPM St.II, DCT, servo tunes
Cosmetic Mods: OEM CF splitters, mirrors, center console, spoiler; Arkym CF diffuser; LUX; tint