Is it possible to bulk fulfill by item number? Example: select and fulfill all orders that contain a single quantity of a particular item.

Not natively. Could be completed through customization though. Operationally you could find the info through saved searches then fulfill the orders, but still manual.

So all your orders have just 1 item? Or do you want to fulfill just 1 line of a sales order if it contains a certain item. And the other lines would be fulfilled later?

The majority of orders have just one item.

In that case you could make a quick workflow that will source the item into a custom transaction body field. Then you could use the native Fulfill items screen and add a filter for your custom transaction body field (which would hold your item number)