AC bias circuit for a tape recorder
Check the type of your recorder erasing head. It's likely just a permanent magnet that saturates the magnetic tape in one direction. It's OK to record to such tape with DC bias, but I don't know how it is suitable for AC-bias recording. Anyway, it's better to replace it with a ferrite erasing head because it demagnetizes the tape and prevents it from producing low-frequency saturation noise.
The bias current is several times higher than the recording current and also its frequency is higher. The head's resistance is primarily inductive at such frequencies, so it makes the AC bias voltage many times higher than the recording voltage or even the amplifier's supply voltage. It means you need a separate bias generator anyway.
The simpliest bias generator circuits contain one transistor, a transformer, and several capacitors and resistors. An erasing head is commonly attached to the generator directly, and a secondary winding of the transformer is capacitively coupled to the recording amplifier output.
You need to know your recording head's inductance, maximum recording current and maximum bias current to design the bias generator.