What is the verb for shoppers buying from a wholesale?

Solution 1:

In the UK it's often called...

cash-and-carry
A cash-and-carry is a large shop where you can buy goods in larger quantities and at lower prices than in ordinary shops. Cash-and-carries are mainly used by people in business to buy goods for their shops or companies. _{Collins Dictionary}

Comparing NGram charts for American and British English strongly suggests to me that the usage was popularised in the UK by American soldiers during WW2. If you compare those two charts you'll see that Brits have continued to use the term ever since, whereas it's become significantly less common in the US in post-war decades. Perhaps that's because as a nation of shopkeepers, Brits have more reason to use the term.

Solution 2:

Bulk-buy is what you're looking for.

Bulk-buy (verb): to buy something in large amounts.

Example: because we're such a large family, we find it cheaper to bulk-buy foods we eat a lot of. - (Cambridge English dictionary)

Bulk-buy (verb): to buy (goods) in large quantities. - (Collins English dictionary)