I don't know if I would have picked up on the BG connection, although naming the Arjuna character "Junuh" might have tipped me off. I am not the kind of person to pick up all the fine similarities, so my coarse view of how BG comes out through Bagger Vance is this:
I think my view of spiritual gifts and service to God has been influenced by the Gita. My understanding of spiritual gifts is that we all have different ones, and our purpose is to use them in service to God. Just as each person has their own dharma (vocation, maybe?), each person may have different gifts. We should not strive to mimic other's gifts, but use what we have been given. As George Fox wrote "And therefore all mind your gift, mind your measure; mind your calling and your work. Some speak to the conscience; some plough and break the clods; some weed out, and some sow; some wait, that fowls devour not the seed". I think we sometimes have a tendency to mistake our calling as something everyone should be doing (although there is also the problem of writing of something important, like business meeting, as being "someone else's calling").
The detachment from the results is also very important. When we do something in order to get a reward, or recognition, we run the risk of feeling ourselves a failure if we don't get what we are expecting. It also means that we may ignore some small act in search of something with a bigger rewards. For example, if one acts faithfully in speaking out against war, the fact that the war continues does not mean that the speaking out was a failure. When one is moved to engage someone one-on-one about war and instead stands on a corner with a sign because it visible to more people, that could be considered being unfaithful to one's calling. Inviting someone to meeting isn't necessarily a failure just because the person doesn't come. That is a difficult thing to remember in our society.