Balanced charge pump (i.e. capacitively coupled bridge rectifier) driven by the secondary feeding your HT rectifier, shunt regulated to your desired bias voltage. Choose the charge pump coupling capacitors to limit the current to only slightly over the max load on the bias supply, at min. AC line voltage, so that most of the voltage drop required is reactive in the coupling capacitors, to keep the dissipation in the shunt regulator's feed resistor fairly low.
N.B. the bias supply will come up relatively slowly compared to the HT supply, which can be an issue if the cathodes are already hot when AC to the transformer supplying the HT rectifier is switched on.