On June 1, 2019 the new California ammunition law goes into effect.
Gone are the days of picking up boxes or cases of ammunition (remember the truckload sales?) and take them to the store counter. You will have to ask the store employee to bring you the ammunition AFTER you pass a background check.
At this time you will not need to have a special permit to purchase your ammo. You will need to be 21 to purchase handgun ammo – 18 for rifle and shotgun ammo.
You will also need to pay a $1 “fee” to the DOJ for every time you make a purchase.
The Bay Area Gun Vault has a good write-up that goes into more detail and restrictions of the California Ammunition Law. See the AMMO LAW FAQ tab on their web site: http://bayareagunvault.com/