What is your configuration setting for 'Settings' - 'Configure OpenLP...' - 'Themes' - 'Theme Level'?
https://manual.openlp.org/configure.html#themes
With the 'Theme Level' set to 'Song Level', it will use theme for a song in this order:
song themeif no song theme, service themeif no service theme, global theme
To make this work, try the following.
Change the settings for your bible to the bible theme you created.
Edit every song and set the theme to the one you created for songs. (or set the song one as the default theme, which would be less work?)
You also need to turn off the Themes setting 'Transition between service items', which will force a transition between items. E.g. when changing from a song to the bible. I think it then uses the theme to decide in a service item whether to transition.
Also keep in mind that if you change the bible theme, you will need to add verses back to the service to get the changes. I believe the same applies for custom slides.