Hello friend, I love growing basil too. Sorry you are having problems with beetles. Pick off any bugs you see and remove them from the area. Neem works but its best to mix a little dish soap to the neem in warm water, to help it stick to the plant. Always use fresh mixed and never old spray that over 24 hours old. The problem with using neem is it tastes bad when you eat the basil.
If you have a lot of bugs, you can use frost cloth to separate the bugs from the plants. Just get enough frost cloth to cover your basil bed and use pvc hoops for supporting the cloth. Cover your plants when the bugs are bad remove them when they not a problem. Good luck.