Using it on a queen would be equivalent to using it on a princess. Every queen carries both the traits of the princess and the drone it mated with, but the traits you see in the bee analyzer are those of the princess only. Changing those traits would NOT override the traits of the drone the princess mated with. To make it clear: if for example you bred a princess with a drone, neither of which were nocturnal, then used a nocturnal serum on the queen, this would be the same as if you had bred a nocturnal princess with a NON-nocturnal drone. Therefore your chances of getting more nocturnal bees out of that queen would be only 50%.
In order to ensure that you will 100% get what you want, you need to inject the serum on both a princess and a drone, then breed the two together.
You do know that serums are re-usable, right? Using it on a bee does not destroy it, you can use it on as many as you want, as long as you have liquid DNA so you can refill it.
But to answer your question in case it absolutely has to be only one bee: If you already have some industrious drones, then I'd say the best option would be a princess. You can breed it with said industrious drones, and so get even more of them.