BMD is a message format created by Atlus. Texts during gameplay in almost all Persona games and several other Atlus entries is completely handled by BMD files. For example, dialogue speech.
TGE'S AtlusScriptToolchain can manage BMD files.
AtlusScriptCompiler is a commandline program that is part of the AtlusScriptToolchain. By providing the following arguments, for example, you can decode BMD files to .msg (messagescript). Both can be modified using a text editor like Notepad++.
AtlusScriptCompiler.exe input.msg -Decompile -Library P5 -Encoding P5
You can then recompile the .msg into a new .BMD file using commandline arguments:
AtlusScriptCompiler.exe input.BMD.msg -Compile -OutFormat V1BE -Library P5 -Encoding P5
The compiler can be downloaded here, along with a GUI that allows you to drag and drop files to compile/decompile them automatically without needing to use commandline arguments.
Another way to edit BMD files is to use BFMessageScriptEditor program. Simply drag a BMD file onto the exe to extract a .msg (messagescript), edit it with your text editor of choice, and drag it onto the exe when you're done. This will create a new BMD file.
One more way to edit and preview BMD files without even decompiling them is to use PersonaEditor program. This tool supports many formats Amicitia (program) does, and can edit FNT files, and BMD files as well. Simply open your BMD file in PersonaEditor and double click it. From here you can edit the file and save it after you're done.