As a retired fire chief and ex-emt, my advise is to NOT move them (unless you are certain there is no spine injury).
What I mean is, if you come across the person laying next to their bike, you have to assume that they fell, and that there is a spine injury. If you observed them fall and hit the ground hard, you assume there is a spine injury. In both of these cases, the rule is to make sure that someone has called 911 and that help is on the way, check for breathing, and if that's OK, then establish alignment and maintain traction and immobilization on their head.
Note that if they're not breathing, it is essential to establish an airway and get respiration going, and if that takes moving their head and causing further damage to their (assumed) spinal injury, then you have to do that. It's no use to preserve their spine from injury if they die due to respiratory or cardiac arrest. Go to CPR.
If it's really hot (and pavement in direct sunlight on a summer day can get hot enough to burn you) well, they can recover from the burns. Recovering from a damaged spine due to being moved incorrectly is not so easy.
If you are certain there is no spinal injury - lets say your riding buddy started feeling weak, got off the bike and sat down, then keeled over (heart attack, heatstroke, low blood sugar, whatever), and you observed this to be the case - then it would probably be OK to move them either onto grass, or put a blanket under them or something. You observed them go down from a sitting position, and could probably assume that there was no mechanism of injury that would damage their spine.
On a similar subject, I was talking to a bicyclist once who told me that his club recommended that all their members write identification information on the inside of their helmets - the assumption being that the emts would find it there and make notifications, etc. Let me tell you, there isn't any emt worth his badge that's going to remove a bicyclist's helmet if he's been in an accident. He'll just do his patient assessment and treat anything life-threatening, apply a cervical collar, slap you on a backboard with head blocks, and transport. The helmet will come off in the emergency room.