Hello everyone! I've created a bundle for one of my clients but I've never actually published a bundle before. What is the difference between a public and private bundle? How do you get your bundle to show up in the list when people search for it?

Taken from the page when you select edit availability

Private bundles are accessible only by administrators of the account. Shared bundles are accessible to any of the Account IDs you list. Public bundles are available to everyone

From that I would suggest that you want either shared or public, if you want to control who can install/use I would suggest shared. I believe that publishing your bundle with either of these options makes it visible