Answer:
Well, a bat mitzvah is a big deal; but you don't want to overdo it and stress the friendship. The amount should be a comfortable amount, probably comparable to a birthday or xmas gift amount. So, depending on circumstances, maybe $15 - $30 - max of $50. (IMHO)
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The Jewish tradition, when giving a monetary gift, is to give $18 or multiples of. The reasoning behind this is that the word 'chai', which means 'life', has the numerical value of 18.