There seems to be a bit of confusion here.
Flygbussarna is a bus service to and from airports in Sweden. From Arlanda airport they operate three routes. They all pick up passengers at three stops at the airport and then take the E4 motorway south, after which they separate. Each route has its own stops in and around central Stockholm.
The most used line is for Stockholm City and terminates near the central train station. This route typically departs every 15 minutes or so until about 02:00 and then a few times during the night. The other routes would typically cease at around midnight and resume in the morning. These routes are for Liljeholmen and Brommaplan respectively. The latter is the only route that passes Kista, which is a district northwest of central Stockholm.
Is Kista where you are going or is it the Stockholm central station? These places are about 12 km apart and are not served by the same bus route.
Flygtaxi is a taxi service to and from airports. This is separate and very different from Flygbussarna. Have you bought a bus ticket or booked a taxi? Where is your hotel?
You can buy passes for public transit (SL) at the airport. There are no passes for 48 hours, but for 24 hours and 72 hours (as well as for longer periods).