This idea came from another bleach game I played but with a few thoughts of my own in it…
Basically after learning your zanpakuto's name and type you will get a new experience type bar but for your zanpakuto and when this bar is filled means when you can completely control your shikai and are free to use it at anytime.
Now to gain experience it would be through normal forest fights and you can get double from fighting a fellow shinigami in the forest. Example, with a normal hollow you will receive the same amount of exp that you get towards your normal experience (for example 100) but with a shinigami you would only get 1 exp and 200 zanpakuto experience.
Also to make it harder to get, you may need something like 500,000 experience points to activate shikai.
Another way would be to break it down to levels so you can have specific power levels for your zanpakuto instead of one big 500,000 experience bar, so then now you can say when you reach power level 10 you can activate shikai.
This can also be turned around to use for bankai whenever you (Neji) start to think up the idea and program it. You just set the experience required like 10 or 100x more. So for example, 5,000,000 or 50,000,000