Consider a prime factor p of your number k*2^n-1. p-1 is not prime, and has a factorisation p=p_1*p_2*p_3*...*q*r, where q and r are the two largest factors.
If r<B1, the factor p will be found in stage 1, if r<B2 AND q<B1, it will be found in stage 2. No random parameters.
In other words: if all prime factors of p-1 are below B1, it's a stage-1-hit, if the largest (and only the largest) is between B1 and B2, it's a stage-2-hit.
Yours H.