> Attached is a drawing with voltages.
If those are the voltages, it clearly is not built as drawn.
> How do I bias this thing
Same as most small stages. You pick bias resistors which will set voltages to reasonable values, pick resistors to pass reasonable currents. (Yes, it is circular.)
You know the 12AX7 with G1 near zero, 2.2K and 100K will set its Plate in the upper half of the B+ range. The FET Follower will, uh, follow: Source sits a couple volts higher than Gate which is at tube plate voltage. If the tube plate can swing, the FET Source can swing. The FET will pass 223V across 44K or 5mA. Hungry, so watch (don't touch) FET heat. There's also 223V*0.005A or 1.13 Watts in two resistors, so half-Watt parts are only good for 29-day warranty, use 1W, 2W if handy.
> the Gate should be around 1/2 B+.
That's for absolute maximum swing with unlimited input.
Here it can only swing what the tube gives it. Looks like 90V up-swing, though the tube is going to cut-off and doesn't want to swing way high. The FET can easily follow that. For Ab-Max swing, you'd pick a lower cathode resistor (even 470r) to get the Plate voltage down nearer half. Except 12AX7 with 100K load can't down-swing very far. Mid-swing computes to 230V, and 223V=230V for practical purpose.
> is the split cathode load acceptable?
If that is what you want. You throw-away HALF your hard-earned Gain and Swing. But in guitar amplifier, that is often a Good Thing. You gain a well-defined output impedance: 11.1K clean, 22K when FET cuts-off, which limits interactions and bias-shift in tone caps.