I have always been afraid of bugs .(Sure, the original sentence may sounds better, but you shouldn't sacrifice clarity for it.) , s o I was apprehensive when I signed up to be a counselor of a training camp atbug filled ( I would delete this; I mean, isn't forest usually filled with bugs?) forest.
It was a big pay off because two summers later I was able to have a great time working in another bug filled forest as a conservation worker.
Therefore if admitted to Barnard I will bring the perspective of a women who is comfortable in her own skin but strongly desires to explore other cultures and ways of living. ( I think it's weird to touch about your university when all they want is your background.)
I might miss the other grammatical error, but I think both of your essays are good.