I've heard two sentences:
I'm a bit shy person
I'm a bit of a shy person
If they are both correct grammatically, then what's the point to add OF in the second sentence?
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The first sentence is not grammatically correct. It could read:
I'm a bit shy.
I'm a shy person.
If the intention is to indicate a smaller degree of shyness then the first one is preferred. The second one indicates you are a person with the adjective of 'shy'. This shows you as an entirely shy person.
In order to indicate this is a partial attribute then 'a bit' is used along with the function word 'of'.
I'm a bit of a shy person.