I don't think you can. If you don't have a Pier A BP, they will not let you onto Pier A as far as I am aware (although usually it is at Pier B passport control where people get sent to Pier A due to location of the "entrances").

I also think you would not want to. It is at least a 10-minute walk (when walking quickly) from check-in to the SAS lounge plus whatever time it takes at security. Then a 10-minute walk back to check-in, through passport control, security, and then a 5-minute walk to your gate.

Just go to the bmi lounge in Pier B (take the lift upstairs 50 metres after security control to the left). It is not quite as nice as the SAS lounge, but you'll be fine.

SmilingBoy.