Unclear, but probably not.
A Bag of Holding is said to create an "extradimensional space". This is not stated directly in its own description, but is made explicit when cross-referenced with a portable hole or Heward's Handy Haversack, each of which attributes this property to the others.
Within D&D, an extradimensional space is not normally accessible without special means. The three items above describe how to access these spaces. Further, an item placed within a bag will suffocate. There is no mention made that the bag mush be closed. This indicates that the interior itself is extradimensional.
Given these restrictions, a strong case can be made that an item in an extradimensional space is not "on your person". The description of wearing and wielding magic items (DMG, p. 140) says:
Using a magic item's properties might mean wearing or wielding it. A
magic item meant to be worn must be donned in the intended fashion:
boots go on the feet, gloves on the hands, hats and helmets on the
head, and rings on the finger. Magic armor must be donned, a shield
strapped to the arm, a cloak fastened about the shoulders. A weapon
must be held in hand.
This heavily implies that an item "on your person" must be physically present "on your person". But these are all extrapolations of D&D rulings and principles. It is not explicitly stated, and so a DM's ruling is required. That is why we have DMs.