I don't believe this works.
The feat Ritual Caster states you choose one class and you can add spells from that Class Spell List to your ritual book.
The Bards Magical Secret does not in any way modify the Class Spell List.
The nice thing about Ritual Caster, is that if you come across a scroll/spell book, it does not care if it is an arcane or divine version (if there is such a dividing rule in 5e), but it must be on the Class Spell List that you chose.
The interesting questions to answer for Ritual Caster are:
Whose Class Spell List has the most spells to offer as rituals?
What ritual spells are you most likely to come across in written form?
The jump to conclusions answer is Wizard: at a fast glance at the page it looks like the largest spell list, and is most likely to be written down in some form.
Without the DMG with rules on how scrolls are actually created or cost to purchase, the known rules for methods to acquire rituals would be: rely on NPC wizard spellbooks, or spellbook/scroll treasure to pick up new rituals.