If you are in Banning you should proceed on east Ramsey st until it become an on ramp and crosses under the freeway (I 10). The last time I checked a map you are allowed to ride on the shoulder at least a short distance (next off ramp). However if you see a break in the fence there is an unmaintained old road between the freeway and the railroad tracks. It's a little rough but has virtually no traffic. Follow this east bound (it changes name to main street after a traffic circle and becomes a better maintained road) until it ends. You enter the freeway shoulder but exit on Hwy 111 towards Palm Springs. Follow 111 towards Palm Springs until you get to the road that goes up to the Tram. Make a left on W. San Rafael Dr. and follow it to N. Indian Canyon Dr. Make a left. Go North on this road until you get to Dillon Rd then go left. Dillon will take you to 29 Palms Hwy (lots of traffic). Make a Right. Follow this until you get to the signs that will take to you to Joshua Tree National Park.
In 29 Palms you can take either Godwin Rd, Utah Trail or Adobe Rd north to Amboy Rd. Make a right (east) and follow Amboy Rd (you will be going through a desert area with absolutely no services) until you get to National Trails Hwy. Go right (east) When you get to Kelbaker Rd make a left (north). Follow Kelbaker Road all the way into Death Valley. The only services on this route are at 29 Palms and Baker. This is a desert area that is very lightly traveled. Carry lots of water.
Once you get to Death Valley you can take several roads east to connect with the Hwy 95 or 160 that will take you into Las Vegas. Unfortunately there isn't a good way to get from Vegas to the Grand Canyon. The most direct way is to find you way east through Vegas to Henderson. Then you can get on Hwy 93 that goes through Boulder. Follow Hwy 93 (wide shoulder) until you get to Interstate 40. That will take you to Williams and the road that goes up to the Grand Canyon.
Most of the area is a desert. Be prepared to carry lots of water and food as there is NOTHING between towns. Most likely you won't have any phone service either.