Keep in mind the following:
- There are benefits to using a particular fighting style as allowed by class. For example the Assissin can fight with a weapon in each hand and thus gains a +1 to attack. A Fighter can use a shield and gain a bonus to AC.
- Further to the benefits granted by the class for what weapons and weapon styles they can use, classes are also granted access to weapon style proficiencies which when taken add their benefits to the ones already granted. In your Assassin example, an Assassin fighting with two weapons AND taking the two weapon fighting proficiency would gain a +2 to attack.
I cannot comment on the Bard as I’m unfamiliar with the class.