It Shouldn't Unbalance Anything... for the moment
For the purpose of simplicity, I'll be mainly restricting my answer to bonus action spells here. This is both because many bonus actions require an action to be done the same turn (such as Two Weapon Fighting), or are unlikely to be particularly useful outside of your turn (such as Cunning Action).
There are two major restrictions on bonus action spells in DnD-5e.
You cannot Ready a bonus action spell.
If you cast a bonus action spell during a turn, other spells you cast must be cantrips with casting times of one action.
With a Paladin character, there's very little chance that the second restriction will come into play often. But with other classes (especially Sorcerers), the second restriction comes into play quite often.
The major concern I'd have with "readying" a bonus action is that it might be used to circumvent the second restriction: but your proposed method will help reduce that worry considerably.
Why it is balanced... for the moment
1. Your Action is still restricted (by being used up)
Normally, casting a bonus action spell limits the use of your Action. Your proposed method (using up an Action, and bonus action to Ready the spell, and a Reaction to release it) similarly guarantees that action economy is maintained. Granted, a Fighter's Action Surge could permit you to still cast a leveled spell on the same round you'd readied a bonus action, but Action Surge can similarly permit for two leveled spells being cast in the same round (without costing a bonus action and reaction).
2. "Readying" a bonus action spell will be inefficient and risky
Many of the bonus action spells available (Magic Weapon, Shillelagh, the Smite spells) are designed to make your Action more effective in combat: to enhance something else you do on your turn. The ability to do these things outside of your turn will not enhance their effectiveness. Other ones (like Misty Step) could potentially be quite useful on turns other than your own: but often they'd be just as useful during your turn. If you suspect you might need to teleport somewhere to cut off an enemy's retreat, you could teleport there ahead of time, and restrict that enemy's options. The fact that you'd need to spend the spell slot of the bonus action spell to Ready it, and maintain concentration on it until it is released, also makes this strategy one which is inherently risky : if you're mistaken, and the Readied spell never gets its trigger (the enemy doesn't run to the bridge, but rather jumps over the gorge), you'll never release the spell, and will lose the spell slot.
There could be some niche situations where you'd want to ready a bonus action spell (e.g. you're worried the enemy might just cut the rope bridge while you're on it, and want to wait until they're on it too), but mostly it will be a highly inefficient use of an Action, Bonus Action, and Reaction. Especially since I can't see any examples of Bonus Action spells which would be considerably more devastating if taken on another creatures' turn... for the moment.
Why I keep saying "for the moment"
Any answer which posits how the rules will change in the future is suspect, as is any answer which posits designer thinking on a topic without quoting the designers. Unfortunately, I'm about to do both, so take it with a grain of salt.
The bonus-action rules on spellcasting are a protection against future problematic interactions. If the game designers think up a cool new spell, but are concerned with how it might interact with non-cantrip spells (cast by the same caster), or concerned how it might be overpowered if used on another creature's turn, they can circumvent these potential problems by giving it a casting time of a bonus action. As such, it's entirely possible that a spell will come into being later which makes this homebrewed rule highly unbalanced and problematic.
By allowing bonus actions to be "readied," we may be removing a barrier to abuse the game designers are counting on down the road. Still, this is a "slippery slope" argument, plain and simple, and shouldn't prevent you, now, from making this change if you so desire (and are the DM/ have your DM's approval). That being said, if you do make this change, stay vigilant for new bonus-action spells in future material: and be prepared to alter this rule further if it becomes problematic.