MusicBee defaults to save play count of each track to MB database file only. But you can save play count to your music files as well and keep them auto-updated. You first need install Additional Tagging Tools plugin and enable it.
Saving play count as tagEdit
1. Go to Edit> Preferences> Tags(1) > custom tags
Choose a custom tag, rename it "P_count" or something, and select a frame the new field will use with the drop-down menu (If you do not change the custom tag setting from "Save to MusicBee database only" to something else, there's no point of doing this).
2. Go to Tools> Tagging Tools> Advanced Search and Replace.
3. Import all presets and find "TOY: 'Copy tag' command" preset.
4. Select all tracks in the main panel and make it to copy "Play Count" to "P_count" field using drop-down menu. Click on "Preview" and then "Apply" if everything looks OK.
5. Tick the box in front of the preset name to make the preset auto-applied to all tracks in your library. Now whenever a play count of a track changes, "P_count" tag value of the file will get auto-updated.
Copy play count tag to MB databaseEdit
You can also copy play count values saved in your music files to that field of MB database. With this, you could update play count values of a new library using the values saved in your music files.
Select files and go to Tools> Tagging Tools> copy tag. Configure it to copy "P_count" to "Play Count" and click on Preview and then Proceed.