Should/can I return a new bike that seems too big?
I think it was downright irresponsible of the shop to sell you a bike that so obviously doesn't fit you. They should have done at least some basic fit testing, which clearly they did not. The trouble is, you're at their mercy now.  Since it's not a warranty issue, they're not obligated to exchange it. So I would be very polite in how I asked, and I'd make sure I asked the manager or owner, not some 18-year old sales guy.  But if they say no, I would push harder.  If they still refuse, I'd get a lot less polite and make it clear I would be very vocal about my displeasure with friends and the biking community, including online sources such as yelp.com.  I would then sell the bike while you can describe it as virtually brand new, and go to another shop that will fit you properly.