If you've ever been to the Supercheap Pharmacy in Phuket town (opposite new bus station), this is the kind of place I am looking for, but in Bangkok.

 

Any insight?

Wholesale? That's for chemists only or do you mean cheap? Lower sukhumvit walk past soi 13 towards Asoke and its the first chemist on the left, cheapest by a mile and I've been to them all in that area

As above - no wholesale for the general public but there are certainly pharmacies that have generics at good prices and will sell in bulk. My favorite is Rung Rote on Soi Onnut (77), entering from Sukhumvit it is on your right about 50 meters into the soi.

Also for many items the GPO pharmacies often have better prices than regular retail joints