Measure resistance and capacitance with bias in low frequency

I have a device which can be modeled with a resistor in parallel with a capacitor. Now I want to measure its resistance and capacitance as a function of voltage bias (from -2V to 2V) and frequency (from DC to 10kHz). Originally I was thinking of using a LCR meter such as handheld Agilent U1732C which can measure in 100Hz, 120Hz, 1kHz and 10kHz. But the problem is I am not sure how to apply a bias and measure with this equipment at the same time. On the other hand, I don't need very high precision. I think 5% precision should be okay. But more frequency points from DC to 10kHz will be helpful. So my question is:

1. How can I apply bias on the device and measure its C and R using Agilent U1732C? (or Can I do that? )

2. If 1 doesn't work, can I do it with a not-so-complicated DIY kit rather than resorting to a high-end LCR meter?

Thanks!

Problem is your meter can measure Cs and Cp but a capacitormodel is Rs of the cap in series with the reactance of that cap. This impedance can be recalculated as a resistance parallel to that cap.
If you add a real resistance in parrallel you will measure the total of the two. I fell in that trap when I got my first Impedance/ admitance bridge. Impedance is the series model Z=Rs+lX, and admitance Y=G+jB. G is Rp

This sort of measurements is the domain of network analysers but it can be done with a impedance bridge. Maybe the 3 voltmeter methode is usable.

A DC bias for most bridges is no problem. I do not know if the Agilent can handle DC. You can place your DUT between to big very high grade caps. Now you can apply a DC bias to the DUT. If you measure the DUT first, then the DC blockers and then all tree you can calculate the rest.