Okay, I was in the National Archives today, and after digging through some old books I managed to find this out:
Till 1939, 1 of May Sweden had 37 Tankers of which 8 Tankers had names starting on "B", they where:
"B.T. 1"
"B.T. II"
"B.T. III"
"B.T. IV"
"B.T. V" (Old name Klas)
"Balaklava"
"Bellatrix"
"Björn"
There was one Tanker with name "Soya", her old name was "Bertil" but this was before 1939.
My next goal is to find out where the ships with the names starting on "B" where during the dates you gave me. But that I will have to do later in the week.

How do You explain that B.T ??? We are looking for possible swedish tanker with name close to Bremen/Bergen (first letter might be different)
P.S.
this is proper post :)

The B.T. tankers belonged to a company named Bensintransport AB (fueltransport AB) so there you have the explanation to B.T ("B"ensin"T"ransport).
Here are the names of the remaining Tankers:
"Abadan"
"Algol"
"Ariston"
"Capella"
"Cleopatra"
"Dalnäs"
"Gustav E. Reuter"
"Hamal"
"Kalmia"
"Lars"
"Nerita"
"Pan Gothia"
"Pegasus"
"Pollux"
"Pratt"
"Procyon"
"Rigel"
"Shell 3"
"Shell 6" (Old name Shell 1)
"Shell 7"
"Shell 21"
"Shell 22"
"Soya" (Old name Bertil)
"Soya II"
"Soya III"
"Soya IV"
"Sveaborg"
"Sveadrott"
"W. R. Lundgren" (Could possibly misstaken for Bergen, almost the same ending)
I can find out, if all of these Tankers operated on the Baltic during those days, but it will take some time. I will have to go to the national archives agian.

Take Your time my friend. We are careful while checking everything.
BTW. I have left msg for You on "gg" my number is 3439782.

Great JOB Polak