My DM is arguing that I need to roll a hit as my bonus action to take an unarmed strike following an attack action (as per Martial Arts or Flurry of Blows). Is this true? I was under the impression that when a monk used a ki point to alter their attack this would be part of tailoring the attack using this ability.
Your DM is correct, the bonus action attack for a monk requires an attack roll.
The relevant rules come from Page 78 from the PHB, under the Martial Arts and Ki sections:
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.
Immediately after you take the Attack action on your turn, you can spend 1 ki point to make two unarmed strikes as a bonus action.
This ability lets you make extra unarmed strikes, but nothing in the feature says that this strike wouldn't require an attack roll. To quote the basic combat rules on Page 194:
When you make an attack, your attack roll determines whether the attack hits or misses.
Any time you make an attack, no matter the source, you must make an attack roll to determine whether that attack hits or misses.
To put in into your "fighting style" context, think of it like a martial artist making two strikes instead of one. Your style might give you the ability to strike twice as fast as a normal person, but your opponent still has the chance to block or avoid the second strikes.