I'm not sure " To the degree that sometimes my bosses were left hanging, waiting for a day or more on my work." necessarily means what you're saying. There are absolutely ways to communicate that you need a personal day - or that something is delayed because [reasons] - that aren't 'just disappearing'.
If you need a personal day then use one of your allocated vacation days. It's still unprofessional to be springing these on people at a moment's notice rather than communicating them ahead of time, though.
If you aren't using a vacation day then you should absolutely be reachable throughout the entire work day, and disappearing for a day at a time is unacceptable.
