I was in Stockholm over the day yesterday. The plane down departed at 06:45 and I came back at 22:10 in the evening. Though I was offered a taxi ride by my employer I turned it down in favour of biking.
It's about 8 km from my home to the airport, a little longer by car I believe. Taking the bike is actually quite a breeze, because there's a protected bike lane all the way. While I do cross some roads it's really just streets with very little traffic. And bikes have the right of way in almost all of those places. The airport even has dedicated bike parking, with a somewhat protective roof.
It took me about 25 minutes to ride each way. A taxi trip would probably be a little quicker but only marginally so. I'd have to be out waiting for the taxi for a couple of minutes, it would pick up another couple of colleagues on the way, and the trip itself takes about 15 minutes by car.
I dressed a bit too lightly for the ride. That was more or less the only downside.
-- CC0 Björn Wärmedal