If you like "adventure", there are two options to go by public transport. Both involve a 20 minutes walk or 10 min bus trip to the Detmold train station.
Option A Bus + Tram (longer travel, less prone to delays), runs hourly (06:05, 07:05, 08:05,..., 20:05)
Bus RE82 SEV from a dedicated bus stop in front of Detmold train station change at the second stop in "Bielefeld-Sieker" (50 min) to
Tram 2 towards "Altenhagen" -- This tram arrives 10 min/ 8 stops later at Bielefeld central station (subway). Plan a 6 minute walk from tram stop to the train tracks.
Option B Train + Bus (shortest travel, more prone to delays), runs hourly (05:59, 06:40, 06:40, 07:40,..., 19:40, 20:40, 22:41)
Train RE72 towards "Herford" and "Lage (Lippe)" from track 2, change at the next stop "Lage" (7 min) to
Bus RE82 SEV -- This bus arrives 40 min later at Bielefeld central train station (back entrance). Plan a 3 min walk from bus stop to the train tracks.
Especially option B is prone to delays: If you miss the bus in Lage, it can happen that you arrive one hour later in Bielefeld! Further, the bus trip from Lage is less convenient.
Please plan ample time if you have to catch a connection in Bielefeld!