After you install MusicBee (I highly recommend the PORTABLE version installed to a folder outside the user permisions jungle, like C:\MusicBee), when at first start it prompts you to select a library file location, just select the mp3's on your C drive, not the external drive.
Which is not to say you couldn't also add the external drive files to the MB library as well--not sure what you mean by a "conflict" with iTunes, unless you are talking about Windows file associations. If the latter, it's true that you can associate only ONE app to open mp3's by double-clicking the file in Windows, no matter what drive the music is located on.