It's not shady, it's actually to protect you and them from fraud.  Given the recent price jumps, the idea of getting money in and out before someone could even verify that you legitimately have funds in the original account is too tempting for scammers.

The easiest way is something like coinbase.  I just bought my first tiny bit of bitcoin through there and they verified my bank account pretty quickly.  Some banks have faster verifications than others.  At least that way, you can get locked in at a price while waiting for the trading account to get verified.