I took the bus to Flagstaff last year- I would not do it again unless I absolutely had to. The bus was late and full of angry passengers who had been stranded in other towns along the way, and stranded them again in Flagstaff in the middle of the night during a snow storm. I know that the bus system back east is at least functional, but in this area I would say it's broken. I'd love to hear if anyone has had a better experience lately.
Greyhound is definitely not traveling in style...it's pretty bare-bones as far as amenities go and as mentioned their adherence to schedule leaves a lot to be desired. I wouldn't worry too much about downtown, though...there will definitely be lots of folks on board and I would imagine at least a few cabs would show up to serve them.
I did it from Dallas to Abq a couple years back. Left in the evening, had a switch in Amarillo and got into Abq in the AM. Couple of smoke breaks along the way, otherwise no issues. For the money you get what you pay. Would I do it again, yes.