Have not built this circuit, but since your goal would be driving the grid of power tube in the same range as a tube driver/preamp, I would use the negative bias supply voltage as (-)Vs. This would give you enough negative swing to place output tube into cutoff. You will have to reduce the source impedance of the bias supply voltage source and insure you have enough supply voltage filtering on place: you would be building a more robust negative supply voltage that could source and sink several milliamps. Typically bias supplies are designed to provide a sufficiently negative voltage w/o much current capability. You'll have a pair of MOSFET drivers operating from this supply (out of phase), and it will have to be stiffer (voltage doesn't change as much with changing current flow). You will choose source resistors (similar to cathode resistors in cathode follower) based on DC operating conditions. In a typical N-chan MOSFET, the source will be 1-2 volts lower than gate voltage.
For (+)Vs, you have a few options. If I were doing it, I'd tap off unused 5V AC heater winding, 6.3V AC winding or use a wall wart in the 9-12V range. You won't need to swing way positive. Full wave rectify or FW bridge the heater windings with capacitive filter and you'll have a (+)Vs voltage.
The MOSFET source follower pictured is DC coupled, so the signal is fed in via coupling cap and DC bias is fed in through the resistor connected to MOSFET gate.
First thing I'd do is look at present tube driver output and see what kind of voltage swing it is generating. You may have to experiment a little. The main thing you'll have to choose is the value of the source follower load resistor. Too large and your signal could be slew rate limited (distorted) - too large and you'll be throwing current away. In this case a little more bias current than is needed is the best bet.
cheers,
rob