You can take an Uber service from your accommodation in Barranquilla to Universidad del Norte. Price will vary depending on the distance. https://www.uber.com/es/cities/barranquilla
A taxi from your accommodation in the north of the city to Universidad del Norte should cost between 6,000 and 10,000 COP. If you are staying in a hotel, ask the reception to call a taxi for you.
Route U30 runs from Estación Joe Arroyo (Carrera 46 and Calle 74) and heads north on Carrera 46 until Calle 100 where it turns onto Carrera 51b and continues north to leave you at the main entrance (Entrance 1) of the university. The cost is 1,800 COP, although passengers must have a travel card to board.
Several bus companies such as Sobusa, Coolitoral, Prado Porvenir, Prado Lujo, Porvenir Paraiso, Urba Playa and Allianza Sodis operate services which serve the university. The sign on the front of the bus will state either Uninorte or Corredor Universitario and the cost is roughly 1,700 COP. These buses will leave you, like Transmetro at the main entrance of the university (Entrance 1).