# Yes.

The [Ready][1] action specifies that

> When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs.

So when you take the Ready action to ready a spell, you have, in fact, used your action to cast a bard spell.  You have "cast the spell as normal," RAW.  This seems to fulfill the requirements for the bonus action weapon attack: you have _used your action to cast the spell._  (I might read it differently if it said "if you cast a bard spell as an action.")

This presumes that you are readying the spell to be cast sometime after your weapon attack but before your next turn.


  [1]: https://www.dndbeyond.com/sources/basic-rules/combat#Ready