Reykjavik University is located next to Öskjuhlíð hill, one of Reykjavík's green areas shaped by the Ice Age. Bus line 5 stops in front of the university (Direction Nautholl - HR, terminal station). You can enter line 5 at Hlemmur, one of Reykjavik's central bus hubs.
You can buy single trip tickets on the bus for 440 ISK. You must pay the exact fare in cash. The driver will not change and will not accept credit cards. If you use the Straeto app, you can register your credit card and use it to pay on the bus. Additional fees may apply for a mobile phone data connection. Multi-day passes and a 20 ride ticket are available at selected places.
During the summer season, buses will run every 30 minutes during the day times.
For more information on local buses, check http://www.straeto.is/en/. You can use the trip planner to check the best route from your hotel to Reykjavik University.