Welcome to American Cycling!
Perhaps from your name you are from Belgium? If so, I understand you are worried. Compared to Northern Europe, cycling in the United States is not well supported by our road system. But, it is possible!
Keep in mind that unlike areas like the Netherlands, many automobile drivers in the United States do not respect cyclists. Because of this, it is important to keep aware and alert at all times to vehicle traffic. Many drivers will, sadly, assume that it is your job to clear the road for them. This can be upsetting at first. But many, many Americans do cycle and enjoy cycling so it is possible to adapt.
When I cycle in Europe I need to adapt also. It can be hard to realize that motorists actually do give right of way to cyclists in some regions! But, it is perhaps a more happy adjustment. :-)
For your immediate question: I am guessing you are in Banning, California? If you are still there, below is a quick suggested route to Joshua Tree based on using Google maps for walking directions. Google is often incorrect for cycling in the U.S., but the walking directions are sometimes helpful.
Perhaps those directions will help you request local assistance.
Another tip is to seek out local cyclists for help.
Google shows a bike shop in Beaumont, telephone (951) 916-4600. According to their web site they are open on Sunday from noon to 4 pm ( 12:00 to 16:00)
1. Head east on E Ramsey St toward S Murray St 0.5 mi
2. Turn right onto N Hargrave St 0.1 mi
3. Turn left onto Johnson Ln 2.7 mi
4. Turn left onto Malki Rd 59 ft
5. Turn right onto Seminole Dr 1.1 mi
6. At the traffic circle, continue straight to stay on Seminole Dr 4.1 mi
7. Turn right onto Kimdale Dr 1.1 mi
8. Turn right onto Rushmore Ave 0.2 mi
9. Turn left onto Tamarack Rd 4.4 mi
10. Slight right onto Service Rd 0.1 mi
11. Turn right onto Whitewater Canyon Rd 0.1 mi
12. Turn left onto Whitewater Cutoff 0.7 mi
13. Slight left onto Old Morongo Rd/Painted Hills Rd 0.4 mi
14. Turn right to stay on Old Morongo Rd/Painted Hills Rd 1.1 mi
15. Turn left onto Windhaven Rd 236 ft
16. Turn right toward Old Morongo Rd/Painted Hills Rd 0.1 mi
17. Slight left onto Old Morongo Rd/Painted Hills Rd 1.1 mi
18. Turn left onto CA-62 W/Twentynine Palms Highway 25.3 mi
19. Turn right onto El Reposo Cir 85 ft