CMOS switch - DC blocking cap necessary?

No. The signal will already be biased about ground. Remember you would connect the ground of the signal to the ground of your circuit.

Essentially you are biasing it if you think of the -V as ground, ground as V and +V as 2V.

What your -V power supply does is actually sorta bias the whole circuit +V. (So gnd goes to V and V goes to 2V)

I don't know which method is best though. I would imagine an additional power supply is not worth it and introduces it's own errors as compared to a cap.

Note though that if the audio does have any dc component it will be transmitted(unless the device blocks it). So ultimately you will need caps somewhere.

like

caps

Ok thanks for that. I'm not sure which kind of supply I'll go with, but I thought I may be able to free up some board space with the dual supply. The other issue is that a blocking cap (and bleed resistor maybe?) might prevent the possibility of clicks and pops being transmitted during switching.

No, They block DC and will let the high frequency through. You need a high pass filter to block the clicks and such(assuming it is higher than audio).

If you end up with clicking from switching(not sure what your doing so I'm guessing) then you need some way to fix it. You can either switch when the signal amplitude is very small or don't transition the switch too fast(this might cause other problems though).