#Yes.
Yes.
The Ready 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.