How to make GABA pass the blood brain barrier?
Short answer
Chemical reversible shielding of the aminogroup in GABA seems to be sufficient to get it into the brain as a Trojan horse. 

Background  

Given that you ask 


  ...how to make GABA pass the blood brain barrier?


I assume that


You wish to elevate GABA by exogenously administering a compound;
That compound has to cross the blood-brain barrier (BBB) and physically turn into GABA;
A drug indirectly elevating GABA through unknown (e.g., GHB) or known mechanisms (Gabapentin) does not suffice your needs.
If you are happy with indirect actions, the links above will help you out. Now on to the real stuff :-)


GABA (Fig. 1) has 3 hydrophylic groups that may prevent it to cross the blood-brain barrier (BBB), namely a hydroxyl-, a keto- and an amine-group. The BBB generally only permits passive entry of small hydrophobic molecules. The amino-group in turn is also prone to de-amination by mono-amino oxidase inhibitors. 

An often-used method to get drugs into the brain is shielding of pesky hydrophilic and/or fragile chemical groups by certain molecules that are irreversibly bound to them. A well-known example of shielding a fragile amino-group is the B-methylation of phenetylamine compounds into their amphetamine analogues. Alpha-amination to a methamphetamine further stabilizes the essential amino-group. Amphetamines and methamphetamines are way more stable in the brain than their phenetylamine precursors and likely enter the BBB also more swiftly because they are more hydrophobic by shielding the amino group (Shulgin, 1990). 

However, those methyl groups are irreversibly bound, so it's not an option here, as apparently you wish to increase GABA, and not an active derivative of it.    

Now, another way is using a Trojan horse method (Pardridge, 2006); by reversibly shielding the essential amine group the drug can enter the brain, where it is converted back to its original compound. Picamilon does the job here. Smarter Nootropics say; 


  First developed in the early 1970s in the Soviet Union, picamilon (alongside phenibut) is an “enhanced” form of GABA that is capable of crossing the blood brain barrier when taken as a supplement.Inside the brain, picamilon is rapidly hydrolyzed into its constituent parts; niacin and GABA. Niacin helps to enhance brain blood flow through its vasodilatory properties [].



Fig. 1. GABA and Picamilon. source: Smarter Nootropics

Reference
- Pardridge, Discov Med (2006); 6(34):139-43
- Shulgin, PIHKAL, Transform Press, U.S. (1990)