One of the reasons Bell turns down the promotion she was offered, besides liking her job and being loyal to her team, is that it fell under the category of "too good to be true". She was being offered a promotion straight from Sergeant to Deputy Inspector, skipping over Lieutenant and Captain, something virtually unheard of in the NYPD. It usually takes 20 plus years of experience to achieve this rank, and an officer usually is required to hold the rank of Captain before being considered for Deputy Inspector. So going from Sergeant to Deputy Inspector would almost certainly carry a lot of strings, it would have put Bell in someone's debt, likely someone one would not want to be in debt to.