Because neither entity names nor bundle machine names are in a database table, there is no official maximum length.
Some entity modules store their bundles in the DB, eg node stores node type with a length of 32, but this is then increased by comment bundles which adds an 11-character prefix.
This leaves contrib modules guessing what to do when they need to store (eg #1709498: lengths of db columns for entity and bundle names are too short).
I suggest that entity API docs should state a maximum length for entity and bundle name length -- say something like 64 -- so anything wishing to store them knows what size field to define.