My perspective: I used to be like you and spend around $250. The bikes would break more easily (although maybe with an insurance/maintenance plan I would have been happier).
Meanwhile, everyone else spends four figures a year on transportation (driving costs about £1000 a year, the tube costs the same). I figured if I would buy an expensive bike once it would justify the cost over many years.
I bought a folding bike (a brompton) rather than a road bike - it cost around £900. They last for decades if treated right. So the cost, divided over the years of use, is negligible compared to other modes of transport.
Don't forget that "good bikes" are actually very rare, especially if counted in volume (not price).
You can buy an adult mountain bike for £80 including 20% VAT in the UK. That's $100.
I've used one like this, it lasted less than 6 months of daily use before the sprockets, wheels, bearings and brakes were ruined.
http://www.tesco.com/direct/north-gear-rxt-mens-adults-mount...
Edit: Sorry, I should have made that clearer in my previous comment.