Unlikely because the Action wasn't to cast a spell. But a DM could rule otherwise.
This spends your turn's Action using Ready. You are using this to cast a spell, but you haven't actually used the Cast a Spell action. You have used the Ready action.
To do so, you can take the Ready action on your turn, which lets you act using your reaction before the start of your next turn...
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs.
In this interpretation, you are still casting a spell with your action, but doing so via Ready. It's off the rails, but only slightly, but I think it's up to a DM because of it...
Because you haven't used the Cast a Spell action, you haven't crossed the gate of spending an Action to cast a spell. You've spent an action to Ready.
Without crossing that gate, you can't use battle magic.
The question is does casting a spell mean completing it or just the cast and energy holding. If you didn't actually use the Cast a Spell, you haven't completed the casting by releasing it. It's unclear as to whether or not you have fulfilled the Battlemagic requirement.
Ready a spell vs cast a spell
The specific difference, for me, is that you are using you're action to Ready. The spellcasting and ready rule requires that you cast to hold with the risk of losing it. But the language is still use an action to Ready. This differs from the language of magical items, such as the Staff of Power which specifically states:
...you can use an action to expend 1 or more of its charges to cast one of the following spells...
In this use of a magic item, you are explicitly casting a spell. With ready, you are readying a spell, not casting a spell. It's a minor difference, but I think this answer hinges on it.
But I don't think it's on the most solid footing, so...
A DM could consider this as casting a spell...because it works without it and has low impact overall.
I don't think it would be unreasonable to allow this. This seems like a capital A attack vs lower case a attack issue and the quote doesn't capitalize "cast a spell."
However, I'm not really sure why you'd want/need to do this as you could just Cast a spell and then use your Bonus Action for Battlemagic attack. You'll have released the spell because you've cast and still gotten your bonus action attack.
If there was a scenario where you want to land the spell after, I'd discuss it with the DM to see if it's a reasonable method and if they're okay with it once or if they are creating an exemption as something you plan on using a lot.
With your particular use case, I'd probably allow this. You're using high-cost resources for low-output attack with the net. There's nothing that really breaks here, it's a neat sequence, and you've burned resources (a 4th level spell slot and lost a net.)
A further note on Bonus Actions and timing
In general, I'm not a huge stickler for order of operations at the table. While I think that the intent is that you use Cast a Spell and not just "cast a spell" in order to trigger the Bonus Action, I don't think that sticking hard to that rule is doing anyone any favors. I've played at tables where we've allowed Shield Masters to take their bonus action first and I think it's just fine. This is a similar case where I'd have no real issue with allowing the Bonus Action attack followed by the Cast a Spell action - especially if it means bypassing mental gymnastics to approve the turn.