During a game tonight, I had a DM state using an action to do a bonus action is allowed by RAW. I was always taught this is not the case. I understand it's the DM's table, but for my own knowledge for my own table, is that correct?
Bonus Actions are in addition to the normal action
This is described on page 189 PHB:
On your turn, you can move a distance up to your speed and take one action. (...)
Various class features, spells, and other abilities let you take an additional action on your turn called a bonus action. (...) 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.
So, you normally can only take a bonus action when you would be able to take your action -- that may be what your DM had in mind. But the bonus action is always an additional action, it is never a replacement instead of your normal action.
You cannot take two bonus actions by using your action and your bonus action, because the bonus action text explicitly says:
You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. You otherwise don’t have a bonus action to take. 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.
The official ruling is that bonus actions and actions are not interchangeable, as per a Sage Advice Compendium entry on the topic:
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.
As Groody's answer also indicates, this is backed up in the RAW by the bonus action section of the combat rules indicating you only get one bonus action on your turn:
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.