My opinion is that I am rarely satisfied with my decisions to buy "budget" items. If I were in your situation...
I would borrow a bow (my sister's?) for a while.
I would sacrifice something else in my budget (coffee, lunch menu $, online subscriptions, etc.) for a while...
And I would squirrel money away until I could buy something worth buying, new or used. $5/week for a year is $250. If I save $10 a week from now until the end of May, I'll have around $200-250.
Once a guy sinks money into a bow, those are funds that -- if he is wise in his bow purchases -- he should be able to get out of the bow when he sells it. That way a $1,000+ bow can eventually become a reality. Buy bows with good potential for resale, and you'll be more pleased each time you upgrade.