No, the Ready action requires taking an Action, not a Bonus Action.
In the section of the rules called Your Turn you can find what you can do during your turn: to sum up, you can:
- Take an action
- Take a bonus action
A special case is the reaction, which can take place on your turn or on someone else's, since it is a response to a particular trigger. Note that the description of the Bonus Action says:
You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available.
You choose when to take a bonus action during your turn, unless the bonus action’s timing is specified, and anything that deprives you of your ability to take actions also prevents you from taking a bonus action.
A Bonus Action can be taken only during your turn, as confirmed by the Sage Advice Compendium:
Can you use the Ready action to take the Dash action on someone else’s turn and then combine the Charger feat with it?
No, since you can’t take a bonus action on someone else’s turn.
The list of the possible actions to be taken can be found here, and in particular the description of the Ready action reads:
Sometimes you want to get the jump on a foe or wait for a particular circumstance before you act. 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.
There are two aspect to consider here.
Firstly, your readied action may take place on another creature's turn (usually, this is the main scope of a readied action). This means that if rules allowed you to Ready a Bonus Action, it still could not take place outside your turn for the rules to be consistent.
Moreover, once you had taken the Attack action, you could not take also the Ready action, because you would have already spent your turn's action budget\$^\dagger\$. You cannot exchange the Bonus Action with an Action, as explained also in the Sage Advice Compendium:
Can a bonus action be used as an action or vice versa? For example, can a bard use a bonus action to grant a Bardic Inspiration die and an action to cast healing word?
No. Actions and bonus actions aren’t interchangeable. In the example, the bard could use Bardic Inspiration or healing word on a turn, not both.
\$^\dagger\$ An exception is the Fighter's Action Surge feature, which allows you to take another Action on your turn.