The original Dungeon Explorer doesn't support save files.
Some games, mainly CDs, allow you to manage your save files.
Since you're talking Turbo, you should pick up a copy of Order of the Griffon. Besides being an amazing Turbchip game, it allows you to see the size of your save files and delete the ones you don't want. The only catch to accessing this feature is that you need to save a file or two until there isn't enough space left for another OOTG save file.
The Tennokoe Bank is a PC Engine HuCard. Since you're talking Turbo, don't bother with one until you get a PC Engine Duo(or equivalent) system. Even if you could use it, all it does is save, swap or delete entire 'banks' at a time, not individual save files.