They already have the roadblock. When entering California from Arizona there is an agricultural checkpoint just inside the state line. I’m willing to bet that ammunition will now be added to the list of questions asked, and probably soon after this law passes they’ll add x-ray equipment.
If it passes both houses and Jerry Brown signs it, it will be challenged in court and an injunction against it will be put in place immediately.
Another ammo law was overturned as unconstitutional a few years ago, thanks to CalGuns Foundation and SAF.