MB does not support direct-syncing to iDevices with iOS higher than 3.11. You need to use either iTunes or "iPod & iPhone Driver" plugin (http://getmusicbee.com/forum/index.php?topic=10634.0). This guide covers how to sync using iTunes.
What You Need - iTunes
You will need first install the latest version of iTunes. But never set iTunes to auto-organize your music files, which will cause MB to keep looking for missing files constantly. Just like MB, iTunes is, by default, not auto-organizing your music files, only referencing them to its database file from their original location. Make sure the top two options under iTunes main menu> Edit> Preferences> Advanced are not ticked. Then it won't copy or move your music files. Also tick "prevent auto sync" option under Preferences> Devices, to control manually what to sync to your iDevice.
To sync the entire MB library, you will need import MB library to iTunes first. There are two ways of doing this. One is exporting MB library file to iTunes, and the other is adding your music files folders to iTunes. The difference is that some fields saved in MB database such as ratings (optional) and play count will be imported to iTunes only through the former method. - For the former, consult "How to export MB library to iTunes" guide (http://getmusicbee.com/forum/index.php?topic=11800.0) and use iTunes's File> Library> Import Playlist command, selecting MB-created "iTunes Music Library.xml" file. - For the latter, use iTunes's File> Add Folder to Library command and select your music files folders. - Then connect your iDevice and select the device from left sidebar. Now choose Music tab from the main window, tick "Sync Music" and choose either "Entire library" or "Selected playlists, etc." Clicking on "Apply" button at the bottom will start syncing the selected songs to your iDevice. - If you want to keep the entire library in iTunes, you will need to update the database file from time to time. To update library, you can repeat either of the same two methods mentioned above depending on your purpose. Note that repeating either method won't create any duplicate music files in iTunes library but the former method (importing library file) will duplicate all MB playlists.
If keeping iTunes library updated feels cumbersome and you don't want to sync the entire library, you can choose to only import playlist(s) to sync. - First, you will need to create exported playlists for iTunes to be able to read and import them. Open MB and right-click on the playlists you want to sync> Playlist Settings, then tick "automatically export a static copy" option to create m3u type playlists under your Library/Exported playlists. - Then open iTunes and delete all tracks from the iTunes library. From iTunes, File> Library> Import playlist, and select the exported playlist from MB's library folder. Then only tracks in the playlist will be imported to iTunes library without copying or moving of actual files. - Now you can sync your iTunes music library to your iDevice. - Whenever you want to sync a new playlist, repeat the steps above by deleting all tracks from iTunes library.