I think it depends on the head, I think*** that typical high end tape heads are designed for AC
It's not the head so much as it's the tape that
needs AC bias. To put it in highly, highly, simplistic terms, the magnetic domains on the tape get 'shaken up' by the bias signal making it easier for the (lower frequency) signal to get them to 'settle' into the new magnetic field you're trying to impose on them.
It is
possible to use DC bias, but that only allows you to use less than half of the (magnetic) dynamic range of the tape. AC bias allows higher dynamic range and less distortion. DC bias in practical recorders is a historical curiosity that probably disappeared while magnetic recorders were still unheard of outside Germany. Basically: no bias = terrible distortion, DC bias = poor distortion and poor dynamic range, AC bias = best distortion and best dynamic range.
To explain it properly you need to talk about coercivity, remanence, BH curves and a whole lot more that I'm not even going to try to get into, if only for the reason that this is ancient history for me and I'd have to pull out the textbooks and revise before even
attempting a proper explanation.
The only takeaway point that I'm going to offer is that proper bias strength and frequency is essential to linearising the magnetisation of the tape, and thus minimising the distortion inherent in the magnetic recording process. The head characteristics will largely set the operating frequency you can use (and physical considerations of tape and track width tend to determine the head characteristics), the tape chosen sets the bias level. Once upon a time I could do a 'line up' - getting the bias level and equalization set for a particular brand of tape - on a multitrack reel to reel recorder in my sleep* but it's so long ago now that I'd have to pull the books out just to work out which knob did what.
And forget 555 timers, this is definitely sine wave territory, in fact low distortion sine wave territory. It's time to learn the joys of trying to get an apparently simple sine wave oscillator circuit to 1) oscillate, 2) do so stably, 3) not generate umpteen unwanted harmonics.
Just had a, very quick, look at that HP app note. Those BH curves are on page 2-3.
This is one of those areas where you can learn a lot from 'the masters' by studying old circuit diagrams. I know for a fact that all the old Revox and Studer service manuals are available online, complete with schematics. By reading the circuit diagrams from several machines you'll soon get a feel for the basic 'how to' and after a while hopefully begin to spot some of the subtleties that make the difference between a design that simply works and a great design that works well.
*And usually did. Studio maintenance is an 'off hours' activity and I'm definitely an owl, not a lark.