So I finally got my bank account verified on Coinbase and bought my first bitcoin, and now it's telling me that it will take 10 days for the transaction to go through. Why so long, and is there a faster method?
It takes a long time because it takes 3 -5 days to transfer money between banks in the U.S. using the ACH system, and Coinbase waits until it receives your money before it credits your bitcoins. 10 days seems unusually long, but it without any details it is hard to comment further.
The fastest method is face-to-face cash through localbitcoins.com or Mycelium's Local Trader, or buying from a Bitcoin ATM. These options are generally more expensive if they are available.