Algorithms for selecting a number uniformly randomly from a subset of integers

Suppose that int array a[i]=i, i=0, 1, 2, ..., N-1. Now given that each integer would associate with a bit. I need an algorithm to uniformly randomly select an integer from the subset of integers whose associated bit are 0. It is assumed that the total number of integers whose associated bit are 0 is already given in a variable T.

One straightforward solution I have is to generate r=rand() % T, and then find the r-th integer whose associated bit is 0 (by testing i=0,1,...). However, I wonder would there be any decent algorithms for doing this? Also, if say that the associated bits are stored in some long int variables (which is true in my case), finding the r-th integer whose associated bit is 0 would not be a easy task.

Thanks for your inputs.