Why do I get a dull ache in my back and legs when I drive?

Ache. Pressure on sciatic nerve due to posture sitting up while driving especially long distances.
Pinched nerve. This perhaps may be a pinched nerve due to muscle spasms or tightness in you lower back muscles. Try adjusting the tilt of the seat as well as the seat you sit in at work.
Inactivity. Having your hips flexed in the seated position for an extended period of time can cause your psoas muscle to spasm. You can reduce that spasm by stretching the psoas(ie lunges) and the hamstrings. If driving long distances, try stretching for 5-10 minutes every 2-4 hrs.