How often I shoot depends alot on the outside ambient temperature...If it's really hot, 90*F and up, I shoot slowly. Anywhere from 2-5mins in between shots. I leave the bolt open, if possible, and keep the rifle out of direct sunlight. I use the underside of my wrist and my cheek to gauge the temp of my barrel.
As for cleaning, I agree with Coyboy as it depending on the age/condition of the barrel. On most days I only shoot 3-4 loads (9-12 shots) per rifle so I usually wait till I get home to clean the barrel(s). If I'm going to be shooting different loads in the same rifle, like going from a Sierra Match King using H4831 to a Nosler Ballistic Tip using RL22, I'll clean at the range. There's no scientific basis for this, just the style I've developed over the decades. I always used a coated rod with an undersized nylon brush and patch (i.e., for .30 cal I'll use a .284" brush). I use a pipette to saturate the patch with Montana Xtreme's Copper Kiler. This usually cleans up my barrels in less than 15 patches regardless of fouling. Good luck. JohnnyK.