score:4
Barranquilla to Cartagena took me just under 1 hour and 30 minutes a few days ago. I did this by bus for 23000 COP which comes to roughly 9 CDN or 6 USD. A few days before I did it the opposite way for the same price and it took 1 hour and 20 minutes.
Taking a taxi you can expect to save time as you wont have to shuffle between the airports and bus terminals. I am not sure if I was charged a tourist price but a 3 hour taxi ride from Cartagena cost me 170000 COP or around 68 CDN, so about 44 USD. Ask an official at the airport for an estimate to get an idea of how much it should cost not to get over-charged.
Upvote:2
The quick and affordable way would probably be to take a cab from the airport (20-25k COP) to the calle 93 with cra 47 and there get in one of the vans leaving every 15 minutes from Berlinas or Marsol. They cost around 18k COP. They leave from the side of the city closest to Cartagena so it should be about the same time as taking a cab. You can also take 2 buses (~4k COP) from the airport instead of the cab but that would most likely take extra 60-90mins.