You can delete an individual base by following these steps:
- In game, tap the gear icon on the right side of the screen
- Tap the 'Manage Account' button
- Tap the 'Edit' button
- Select the 'Delete Base' button under the base you would like to be deleted - this button only appears under bases that are not currently selected
Note: Base deletion is permanent, so make sure you're certain before you go through with it.