how does interelectrode capacitance reduces bandwidth?
Think of a capacitor as a bucket you can fill with charge. It's not so far fetched; the first capacitors were glass jars lined with metal foil (Leyden jars) and until the 1920s, capacitance was measured in "jars" (1 jar is about 1100pf!)

The book is correct - the capacitance is always there and frequency has nothing to do with it. However the charge it can store is proportional to voltage (as if charge was a gas you could compress, not a liquid. And indeed voltage used to be called "pressure".) 

Q (charge) = C * V.


But now consider an AC voltage across the capacitor. In one AC cycle, you fill the bucket, and then empty it. You have transferred charge Q out of the voltage source.

Now the more often you do that, the more charge you transfer in a second.  Charge per second is simply current, so the higher the frequency, the higher the current. 

Current through the capacitance increases with frequency - so the "bucket" conducts better - i.e. its conductance is proportional to frequency - but the capacitance is the same.

Reactance is the inverse of conductance, so reactance decreases with frequency.

(The pedant will note that I should have used the word "susceptance" in place of "conductance" here; 

susceptance = 1/reactance
conductance = 1/resistance


and for completeness,

admittance = 1/impedance


but I think that would only have obscured the basic idea)