Changing the data directory is currently not supported from within Mailbird, however there is a relatively easy way to accomplish the same thing if you don't mind fiddling with Windows a little bit. We of course take no responsibility if you break anything though :)
The answer is to move the data directory to where you want it, then create a hard symbolic link from the original location to the new location. In the eyes of Mailbird, nothing has changed, but in reality your data directory has moved. Note that Mailbird has a separate data directory for each Windows user on your system, so if using Mailbird from multiple user accounts, you need to do this for each user individually and to different locations.
Please refer to this guide for creating symbolic links in Windows:
First, set Mailbird to not run on startup, and then restarted my Windows 10 desktop PC.
To find the data directory, open Mailbird and hold down CTRL and SHIFT while clicking on the main menu. This will enable a hidden item called 'Open Data Directory'. Click it, and Windows Explorer will pop up and open the folder.
Now, shut down Mailbird and move the entire folder somewhere else and create the hard symbolic link.
For instance, if my Windows user name is: 'John Doe', and I moved the data directory to 'C:\Mailbird Data' I would set up the symbolic link by typing this in the Windows 7 command line (note the quotes around the paths to the folders, as there are spaces in them):
mklink /J "C:\Users\John Doe\AppData\Local\Mailbird" "C:\Mailbird Data"
Now if you try to go to the old data location you will actually go to the new location instead. That's it! You have successfully moved your data directory.