My new supported spindle was sold on its own. Bowls for support were sold separately. Such a bowl could cost as much as the spindle.
I didn't see a bowl that really grabbed me. As I said, stock was low.
I knew from books that traditionally a supported spindle could be spun on such humble spots as the bowl of a spoon or the curve of a potsherd. (Bizarre word, potsherd. As in, shard from a pot. You know anyone who says potsherd has been listening to the King James Version of the Bible. Did you know the King James Version was done four hundred years ago, in 1611?)
I found that my favourite footed ice cream bowl worked well enough to support the tip. There is a slight depression in a ring at the bottom of the bowl. I could set the tip there and keep the tip in place. (In the photo, the spindle is laid at rest across the bowl.)
Nevertheless, I was open to new and better options.
At a kitchen shop, I found an egg cup with a shallow cup. The shallow shape is very much like that of a proper, purpose-made spindle support bowl. Works even better than the ice cream bowl. The cup is smaller: the spindle tip doesn't skid around. The base is wider: the cup is more stable.