I was pleasantly impressed by my first trip ever on Greyhound on its Calgary-Edmonton route. The buses were very clean with nice, comfortable leather seats that have more legroom than you'll find on most airplanes. The bus also has the added perks of power plug-ins and free wi-fi. Greyhound employees in the terminals and the drivers were all very friendly and professional.
As a single female traveller, I felt perfectly safe on the bus and in the stations. Due to a few unfortunate past incidents elsewhere in the country, I believe Greyhound often gets an undeserved unfavorable reputation.
For a third of the cost of Red Arrow, Greyhound will be my preferred bus provider for traveling between Calgary and Edmonton. I encourage others to give it a try. You might be surprised by how nice it is.