Every golfer has faced a shot where hitting the ball high and through the air just doesn't make sense to reach the target.
Most commonly, a hole location is tucked on a shelf or so far back on the putting surface that hitting a shot through the air and with imparted spin could cause the shot to come up short of the intended target. A situation like that one calls for a shot that can run along the ground and roll up to the target instead of hitting and stopping. That's when a golfer needs a bump-and-run shot in their arsenal.
A bump-and-run shot and a punch shot aren't all that different of an idea, but the execution and the situational use of each is often quite different. You're going to need a punch shot to get out from under or around a trouble spot, like a tree or a branch. You're going to need a bump-and-run to get to a target where running the ball on the ground is a better idea to reach the target than get there through the air.
Hitting a bump-and-run shot is pretty easy to do, and there are multiple ways to do it.
How to hit a bump-and-run shot
The key to executing the bump-and-run is setting up for a de-lofted strike and trying to impart less spin on the ball than normal so that you get the intended bounce and subsequent rollout. If you can practice this shot with multiple clubs and figure out how the ball rolls out for your style, then you can master this shot.
I prefer to hit the bump-and-run shot with my lowest-lofted wedge -- and not that wedges that come with my iron set. I want to use the wedges that you buy separate from your iron set, as they typically have a groove profile that covers more of the face.
For most chip shots, a golfer is going to set the wedge on the ground on its lowest point on the sole, exposing the bounce and letting that relief and the loft do the work to get the ball in the air. We don't want that on this shot. We want the ball to launch lower in the air, skip or bounce off the ground once it hits that target and then start to roll toward the target and let the spin imparted bring the ball to a stop. Ideally, this means we want less spin on the shot.
With that in mind, the set up for a bump-and-run is practically the opposite of a normal, stock chip shot. We want to sole the club with the leading edge, not the bounce, and with more of the toe on the turf than the heel. This will set us up for a de-lofted strike. Even better is to set up the ball so that it's struck closer to the toe. This will impart less spin on the part and allow for an easier time skipping the ball to the target.
From there, you'll want to stand a little closer to the ball than a chip -- more like a putt. You'll have the grip or handle of the club slightly ahead of the ball. Then you're basically going to take an elongated putting stroke and strike the ball toward the toe. You'll have picked out a target that is significantly shorter than the end goal, as you'll want the ball to skip and the run out. How much spin you impart on the ball can be impacted by how close to the center of the face that you hit the ball and by how quick of a stroke you make. A lazier, longer stroke will result in less spin and better runout. A shorter, more intense stroke will lead to more spin to the same target.
Some golfers prefer to use a higher-lofted, numbered iron, like a 9-iron or an 8-iron. They'll lean that club forward from the grip or handle, often grip down the shaft, take the club back to hit it the approximate distance through the air they want (which is well short of the final target) and then clip the ball.
The danger in using a club with this kind of loft, especially to a relatively short target, is that the golfer will put too much spin on the ball by taking a shorter, faster stroke. The ball then comes up short of the target because of the spin imparted. (Sometimes this is a great option for a shorter shot.)
The other danger is hitting it with not enough loft, so that it comes out more like a putt that can stop short of the target.
However, for a longer target, the numbered iron is a great idea. Executing the same style of shot as you would with a wedge, this shot will go farther initially and then still have a significant first bounce before bouncing and rolling out to the target.