What rusts aluminum nails faster

Rust is defined as iron oxide, the coprrosion product of iron, Eric. So aluminum can never "rust", although it can certainly corrode.

You need to accumulate all the facts you can before you start speculating about chemical reactions. One of those facts is that aluminum is amphoteric (it dissolves in both acid and alkali). Another of the facts you need is what bleach is. Do you know the mixture?

Chlorine bleach does its bleaching by exposing the fabric or whatever you wish to bleach to chlorine. Chlorine is a gas which will not stay dissolved in water of neutral pH. To keep the chlorine in solution in commercial bleach requires that the pH be kept very high, i.e., that the solution be strongly alkaline.

Ted Mooney, P.E. finishing.com Brick, New Jersey

Your aluminum nail is NOT pure aluminum, so you need to find out what alloy it is and then find out what the alloy elements are. A practical example: Pure aluminum reacts very slowly with 50% nitric acid, but will destroy 2024 welds in a matter of days.
Concentrations can be critical, so you have to define what each one is and why, or the project is worthless. Then, do you have to look at any other concentrations?

As Ted implied, aluminum will dissolve rapidly in a high pH solution, so for a given pH, what is the effect of the chlorine? DO NOT ATTEMPT TO LOWER THE pH OF A BLEACH SOLUTION! The gas formed can be lethal and the reaction can be violent!
Look up reactions of chlorine gas with metals (your physical science book to start with). Steel wool will burn in chlorine gas.
Another factor you need to consider is the initial strength and the final strength of each solution. As you said, bleach was a rapid reaction, so you have lost a great deal of the bleach as it reacts with the nail.