Dortmund (approx. 100 km from Bielefeld)
From Dortmund airport there is an Airport Express bus which starts at 4.30 am until 9.30 pm and leaves every hour to Dortmund main station (travel time approx. 25 minutes) - or you can take a taxi. From Dortmund main station there are trains (ICE and IC) to Bielefeld, usually every half hour (travel time approx. 50 minutes). As alternative, there are also Regional trains which leave Dortmund main station once per hour (travel time approx. 65 minutes).
Hannover (approx. 110 km from Bielefeld)
Intercity trains from Hannover to Bielefeld leave at least every hour. The journey takes approx. 50 minutes (it is not necessary to change trains). You can take the S-Bahn (No. 5, departs every 30 minutes - duration 12 minutes) or the airport tansfer bus from Hannover airport to the City Air Terminal at the train station (departures every 20/30 minutes, travel time approx. 25 minutess) - or you can take a taxi.
Düsseldorf (approx. 190 km from Bielefeld)
From Düsseldorf airport there are direct connections to Bielefeld. The ICE leaves every half hour during day time (duration approx. 1 hour and 40 minutes). On some connections you may have to change in Dortmund, with the connecting trains stopping at the same platform.