You can use either two 1N4148 diodes in series or a single infrared LED to achieve a cathode bias of 1.1V. Brian Fox has done formal testing and reports that the IR LED doesn't stay "open" at lower current draws, so maybe the 1N4148 diode is a better option here. I don't want to misquote Brian, so I'll send him an e-mail to see if he can provide a more accurate description of what's going on.
The basic idea, though, is to replace the cathode resistor/capacitor with an LED or diode. Just like with having a resistor running from cathode to ground there is a voltage drop that occurs across the LED or diode that provides the biasing voltage for the cathode. The difference, though, is that with the LED/diode the voltage stays at the same level (it is fixed) regardless of the current draw of the tube. When using a resistor, the voltage changes as the current draw of the tube changes (due to Ohm's law V=IR) so the voltage is not fixed with that configuration.
The key to having this work is to find an LED or diode that will provide the correct cathode bias voltage.
As to whether or not this is "better" it is really just a matter of taste, so try it out for yourself and see. I personally think that it sounds much better than the typical cathode bias with the R/C. Punchier and more phase coherent is how I would describe it, but maybe I'm kidding myself.
I also switched the circuit in my diy Telefunken-Ela-M251E-style mic so that it now uses an infrared LED (and an old Blue Kiwi capsule):
http://www.treblebooster.com/m251e/telefunken_ela_m251e_circuit.htm
Again, I like the sound better, but your mileage may vary....