There are plenty of options on AirBNB with internet in Baranquilla. I just looked to confirm.
When you go on their site and search under Baranquilla, you will see a list of filters near the top of the page right under the search bar.
- Click on "More Filters"
- Scroll down to "Amenities"
- Click on "Show all Amenities"
- Wifi is one of the options.
I did that and plenty of nice places showed up.