In 2010, we used mapquest to find the "best route" from Tucson to Bishop and it routed us through Los Angeles (well actually I-10 to San Bernardino and then up the Cajon Pass. We then used Mapquest to figure time and distance for 3 routes:

Via Blythe and Los Angeles - 683 miles, 10 hours, 30 minutes.
Via Las Vegas - 676 miles, 11 hours, 13 minutes.
Via Blythe and Barstow - 715 miles, 11 hours, 2 minutes

Our take on this is that the time and distance are essentially the same, the big question is which big city you felt like driving through (and what scenery are you in the mood to enjoy). Driving through Barstow avoids all the big cities and is my choice of the three.

My 2000 Tacoma Pickup with a V6 and manual transmission gets about 18 miles per gallon on the highway based on the following spot checks from my driving log:

Gila Bend to Parker: 158 miles, 8.29 gallons -- 19.06 mpg
Wickenburg to Tucson: 272 miles, 15.33 gallons -- 17.74 mpg
Tonopah (Arizona) to Tucson: 200 miles, 10.9 gallons -- 18.35 mpg
Parker to Tucson: 284 miles, 15.18 gallons -- 18.71 mpg

Rounding the round trip distance up to 1500 miles, this means that I will burn 83 gallons of gas doing the round trip from Tucson. At current gas costs of $3.50 per gallon this will cost just short of $300 dollars. Sobering!