does an inmate at federal detention center wait for a bed for residential treatment at detention center? how long does it take?

RDAP is not available at every federal facility. Most of their detention centers do not have RDAP. In all likelihood, if your inmate is already applied and approved, they will transfer them to a facility that has the program when the inmate is at least 27 months from the door. The program is nine months, there is an automatic 6 months of halfway house (the released inmate must take additional classes during the halfway house stay call TDAP) - since RDAP awards inmates that successfully complete the program a full 12-months off the sentence. So 9 + 6 + 12 = 27 months.

I took RDAP in FCI Miami Camp, if you have additional questions we are here, our answers are free. Don't pay one of these consultant websites $5000 or more for this exact same information. They cannot do anything special for you - they cannot make things move faster or tell you something magical to gain an edge.  There are no special tricks to this - save your money.