The attached publication may help but will not provide the exacting detail, step by step process sought. Nonetheless, if you have not decided on an exact approach, it does do well at supplying information and various methods for downscaling elements of climate including rainfall and lists various options, limitations, assumptions, and includes some possible software aids.
In my masers research i performed bias correction of both temp and precp variables for Sikkim (which is hilly region). The performance of the method was satisfactory. The step by step approach is given in the section 2.5 of the attached manuscript. I hope you can use this for your research.