Levodopa is transported across the blood-brain barrier by a protein called LAT-1 (L or Large amino acid transporter) This transport protein operates by what is called facilitated diffusion.

What that means is that if the concentration of levodopa outside the brain is high compared to the concentration inside, transport will from outside to inside. On the other hand, if the concentration of levodopa outside the brain is low compared to the concentration inside, transport will probably be from inside to outside.