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At Tegel, enter the Bus TXL in the direction of S+U Alexanderplatz. This bus leaves every 6-7 minutes, so just go into the first bus in that direction. Leave the Bus at S+U Brandenburger Tor.
At Brandenburger Tor, take the S2 rapid transit train towards S Bernau. This train leaves every 20 minutes, so again the best bet is to simply take the next available train. Depending on where your hotel is, leave at S Bernau-Friedenstal or S Bernau.
"S+U" means a station for rapid transit trains (S-Bahn) and undergroud trains (U-Bahn). "S" is just the rapid transit train. At Brandenburger Tor, follow the signs for S-Bahn platform 2, not for the U-Bahn.
You can buy a ticket for β¬3,40 from the bus driver.
If there are delays, the last possible connection would be the Bus X9 leaving Tegel at 0:29 Monday morning, with transfers at Jungfernheide to the S41 and at Gesundbrunnen to the RE3 local train.
Upvote:0
I am somewhat confused by the recommended route. The U-Bahn does not go to Tegel Airport (TXL). It is served by local and express buses. Looking at the map a reasonable routing is the TXL Express Bus to the Hauptbahnhof [EDIT: As @o.m. indicates, this should probably be Brandenburger Tor], change to the S2 for Bernau. You can also save distance but change twice by leaving the bus for the S41 at Beusselstr. The bus runs until 00:30. The S2 is shown on the night route map, so presumably has 24 hours service. There are also regional trains (for example RE3) from the Hauptbahnhof to Bernau. You can ride them with tickets for the tariff zone ABC too.