Braking distances on a rainy road

I think there is not one general method to calculate this just because its too complex. If there was one F1 engineers would have an easier job.

Nevertheless you can guess $\mu$'s dependence from the data, as you pointed out, if you plot it. I just did it here

http://genflux.chartle.net/embed?index=47502

and seems an exponential decay which, makes sense. As you increase the velocity your tires will lack of adherence due to less contact. So my first guess is that you can write

$$\mu = e^{-b |\vec v|} + a \quad ; \quad a > 0, \quad b>0 $$

where $a$ and $b$ will depend on the data to be fit (your tires and conditions).

Using the answer provided by fénix, I came up with a sufficiently good estimate of the data.