OP, your best bet to make RB simple syrup would probably to use the original stuff (Krating Daeng - you can find it cheaper than on Amazon though) instead of the derived version (Red Bull). It's made with real cane sugar so it should produce a better quality syrup AND give you something a little original to brag about.

Plus it actually does taste better. A,d you can put it back into the little original glass bottles for storage in the fridge.

Edited for typos + link to product.