We were the idiots who took the bus from the airport to Reykjavik (never again!) Then another bus from Reykjavik out to our Airbnb. Then dragged our bags in the snow (again we were there in February) up a hill and 4 blocks down to find our place. It was HELL! The first bus from the airport into Reykjavik took 1.5 hours to just leave the airport because they wanted to fill up with more passengers!
We had previously rented a car for our second week in Iceland for our drive along the south coast, but we thought we might as well use the bus to get in and out of town during that first week.
Then we happened to be in Iceland during a cold spell with snow and we realized that relying on the bus would add up to roughly $36 a day! Transportation isn't cheap in Iceland. So after one round of bus travels, we decided to rent a car while in Reykjavik.
The smaller, non-4x4 car (we were staying in town, so we weren't' worried about not having a billion horse-power) cost us about $30 a day, and made our life so much easier. We could come and go as we pleased into town. You never know what the weather will do, so it was such a huge help during the storms. Grocery shopping was much easier too! Car is the best transportation option in Iceland. Also, there is no Uber, so don't plan on that!
If you're determined to use the bus though, you do so by downloading the app (Android, Apple) that will give you the routes, times, and also acts as the ticket (you show the screen to the driver after activating the ticket).