There isn't a BMW Motorrad dealer in Cartagena. Assuming you are coming from Cartagena and also that you really need a OEM dealer, then think about going to Medellin. That city is closer than Bogota... Also the dealer in Barranquilla is closer to Cartagena, but that is in a different direction...but a nice place.
In any event, call ahead and see if they have the part(s) you need.
Case in point, a helpful parts manager in Sao Paulo BR called around town for me...he found everything I need after speaking to the fourth Motorrad dealer. Yeah there are 4 dealers in Sao Paulo. Stop in the Cascaras VN dealer to buy a oil filter, only to find they didn't have one on the shelf for a F800GS. Yeah, calling ahead can really be worth you time. If you need something simple like wheel bearings, oil or brake pads, get them at a generic motorcycle parts store. You'll save cash, but may spend more time hunting for somethings. Brake pads at the dealer in Quito EC cost ~$90 USD. Tried to find them in Armenia, CO no luck. Found them in Cartago, CO for ~$32 USD. I had some help from some wonderful Colombian bikers and the search was a lot of fun.
If Routa 40 doesn't have it, then keep dialing for dollars until you find what you seek. Or keep dialing for pesos. =) Routa 40 has a great reputation. I stopped for a common bolt to two. They hooked me up, no charge. Really nice people.
Routa 40
(57) (4) 448 18 40 / (57) 310 508 17 31.
info@ruta40.com.co
Cra. 43A 30 26 (Av. El Poblado).
Ubicación geográfica (Colombia - Medellin)
Coordenadas GPS: N 06° 13' 48.3 " W 075° 34' 11.0"
Lunes a Viernes de 7:45 a 18:00 / Sábados de 9:00 a 13:00.
Here is a list of all Motorrad shops in Colombia, tel# and GPS digits. Google the shop names for email addresses if you don't have luck calling.
Colombia
Bogota | Autogermana +571-657-8080 | N4 42.24083 W 74 1.73107
Medellin | Autogermana +571-4-2620140 | N6 13.28693 W 75 34.18117
Medellin | Ruta 40 +571-4-4481840 | N6 13.80528 W75 34.18068
Cali | Auto Bonn +571-2-6838175 | N3 28.76797 W76 31.5594
Barranquilla | Automunich +571-5-3670150 | N11 0.00053 W74 50.4915
BTW - If you looking for service, the good news is most Motorrad dealers will put a traveler at the top of the schedule. Unless you stop in the huge dealer west of Rio de Janeiro BR. Those clowns keep my bike for four days before saying nothing was wrong + no charge. The dealer in Sao Paulo figured out in minutes that I had a chipped tooth on a sprocket. Or you might pull into a dealer and find 3 other travelers got there ahead of you in the service queue (yup, happened in La Paz, so I rode to Lima...)