Well, a bias line is a circuit component that should have as high an impedance as possible, so as not to load down the main line. With transmission type bias lines, there is only one frequency where it truly looks like very high impedance, such as the frequency where a grounded stub is λ/4. That simple bias stub at the frequencies where it is not λ/4 will look either like a shunt capacitance or inductance to the main line. This shunt reactance will reflect rf signals in the main line, causing what looks like limited operating bandwidth of the bias circuit.
So lets say we are at a frequency off from the center frequency, say where the gronded stub is 0.2λ in length. Its impedance of the bias stub is going to be around j 3.0 * Zs, where Zs is the stubs characteristic impedance. Lets say you used a stub characteristic impedance of 70 ohms, so Zs is j 210 ohms.
If you used this bias stub on a standard 50 ohm transmission line, loading it with a reactance of j210 ohms will cause some reflection.
Lets say, instead, that you used a transformer to transform down to a 20 ohm chanracteristic impedance, attached the bias line, and then transformed up to 50 ohms again. Now you have j210 ohms loading a 20 ohm line, which is a much smaller reflection than j210 ohms loading a 50 ohm line. The end result--your bias circuit has a 2.5 times as much bandwidth now.
More practically speaking, lets say you have a bipolar transistor with an output impedance of 10 ohms. If you attached you bias line right there at the transistor output, that bias line reactance will have very little loading effect.
Lets say, instead, that you use some matching network to match the transistor output to a 50 ohm system, and then added the same bias line structure, you would see 1/5 the bandwidth since it is loading down a much higher impedance point.
So think of the matching structure as a standing wave of voltages, find a practical place to add the bias line where you have the a voltage minimum, and stay away from where the voltage maximums would be, and you will have wider bandwidth.