The fastest rail route is through Madrid. It needn't be terribly costly if you buy the ticket in advance. When are you traveling?
ALSA runs buses, but they take a long time. If you opt to travel that way, try pricing out two separate tickets to and from Murcia. After I bought my through ticket, I noticed that I could have saved money by doing that. I guess there must be some sort of special deal on intra-regional tickets. The fellow in the ticket booth was surprised when I showed him the prices on the vending machine.
I bought that bus ticket not long before my trip--probably the day before. I've seen Spanish bus tickets that were a lot cheaper if bought well in advance. I have no idea whether that might apply to the Valencia-Granada route.
The ALSA buses are comfortable, but honesty forces me to report that there's a rogue driver on that route who, if he heads out late, will try to get back on schedule by skipping nearly all the comfort stops. Be ready to hop of the bus and run (literally) to the toilet.