Is she being unreasonable?
Nah. One good bow (which you already have) and a couple hundred arrows per year. You're gold.
Last bow I bought cost me $80 and it's a joy to shoot.
Be sure to save $100 or so for hunting licenses.
Seriously, I don't know your finances or budget. If you are able to make ends meet, have your credit cards current and the mortgage is being met maybe $1,000 is tight.
If you spend more than you make, have nothing salted away, have the cards maxed out, have 59 interests and your paycheck never makes it home - maybe she's a saint and overly generous.