He CANNOT make a bonus action!
The Ready action (Sage-Advice Compendium)
If you want to wait to act in response to something, take the Ready
action, which lets you take part of your turn later
Ready Action (PHB pg. 177)
you can take the Ready action on your turn so that you can
act later in the round using your reaction. First, you decide what perceivable circumstance
will trigger your reaction.
The Ready action allows you to declare a specific instance, and wait for it to happen in order to use your reaction later in the round.
A reaction is an instant response to a trigger of some kind, which can
occur on your turn or on someone else’s.
Because you are taking the ready action, you are using your turn to wait until someone else's turn in order to trigger said reaction. The ready action would not be considered your turn, because you used your turn to take the ready action, and you are now waiting until later to use the action that was prepared on your turn.
In response to a seperate question in the Sage-Advice Compendium, the answer simply stated:
No, since you can’t take a bonus action on someone else’s turn.
Because the Ready action requires you to wait until someone else's turn, be it enemy, friendly, or even environmental, it is not considered "your turn" and you cannot use a bonus action because of this.
Martial Arts (PHB pg. 72)
When you use the Attack action with an unarmed strike or a monk weapon
on your turn, you can make one unarmed strike as a bonus action.
This states that it must be "your turn" to add this bonus action, which you cannot take. Additionally, it also requires you take the Attack action in the first place, which you are not as you are taking the Ready action to prepare an attack, which is not the same as taking the Attack action.