I'm sorry, but this is a gross oversimplification. The only way I can explain how bias worked, in a few words, is this: magnetic recording is, inherently, highly non-linear. By using an AC bias signal (typically >8× the maximum audio frequency of interest) whose magnitude was significantly higher than the wanted audio, as the tape entered the magnetizing zone of the head it would be pulled and pushed through several non-linear cycles of the bias waveform which gradually reduced to zero plus the required audio as the tape left the vicinity of the head.
In the absence of the bias signal, the residual audio would be entirely at the mercy of squat S-shaped hysteresis loop but the fact that the magnetizing force on the tape builds to a peak and the opposite peak and the opposite peak and the opposite peak and then declines gradually at a rate several times higher than the maximum audio frequency leaves a residual that is a relatively linear approximation to the audio waveform you want to record.
Ages ago, you may remember Hugh Ford, of sainted memory, who was an expert in the forensic evaluation of tape recordings. I think he was one of the people who analysed the Nixon tapes after Watergate. Anyway, he published one or more articles in Studio Sound on forensic analysis, and bias continuity was one way of checking whether a tape had been edited. Bias leaves a signature on the tape, and any discontinuity in this indicates that the recording was stopped and restarted, and/or erased and recorded over, so bias does leave traces on the tape, but well down into noise levels.
S.