Two-Weapon fighting and REACTION

I feel like this has been beaten to death, but I'm looking for specific confirmation on this because I argued with a DM that claimed that a rogue who was using two short swords for two weapon fighting and who took a READY action to do an attack when a monster came in the door could NOT take a bonus action to use the other sword. 

I argued that bonus action can go ANY TIME during the round and if he waited to take a REACTION he could use it immediately after that. 

Who's correct?

The DM is correct. Your Action and Bonus Action can only happen on your turn. For pretty much anything you'd do out of turn aside from snarking at the rest of your party the BBEG you need to spend your Reaction, such as to take the course of action you specified when taking the Ready Action.

Various class features, spells, and other abilities let you take an additional action on your turn called a Bonus Action.