I suspect that PayPal has had more of an impact on WU than Bitcoin since PP allows users to move money for free. Moving money by Bitcoin still requires too much complexity for the mainstream compared to WU, especially for American users. Keep in mind that WU appeals to low-end money movers. Businesses like WU are still the only way to move money without involving a money-handling account.
I e-mail money to someone using Coinbase. It asks them to sign up with an account to retrieve the money. Not that difficult.
Once we both have accounts, I can SMS text money to someone using their phone number by saying "Send $2 to 123-456-7890".
Really not that difficult. I think people underestimate what some of these Bitcoin companies are doing.
As evidenced by people in this thread, it is WAY harder to use Western Union or even Paypal.