One of the primary differences between the floor press and bench press is that the floor press is a pure press, no lower body involvement. This appears to be a hybrid between the two so apart from possibly some benefit of the limited range of motion I'm not sure why you would do this rather than just bench press normally
I love the bridge press. It was an old timer strength move. George Hackenschmidt put up impressive numbers, as did Billy Lilly and Joe Nordquest, when it was known as the Belly Toss. This was the early developmental years of horizontal pressing, before the bench, then there was the floor press, pullover and press and bridge press. Bret Contreras, Pavel and Chad Waterbury are a few modern strength coach who advocate it. Strength Writing great, Charles A Smith lists it as one of the great movements for "Full Body Strength" in this article
here. The Tight Tan Slacks of Dezso Ban: All Round Body Strength - Charles A. Smith.
if you're worried about Smith's credentials, also note the 3 other exercises he recommends: the get-up, the swing, the one leg squat...sound familiar?
Pavel refernces it in PTTP; Professional as a great bench press assistance lift that teaches the lifter to use his/her legs and lift a heavier weight than he can flat press. The decline angle also is easier on the shoulders.
Use also do not need a rack to perform the lift, a crucial aspect for a barbell only lifter who doesn't have space/time for a gym or rack at home. It is easier to wedge between the bar and the ground due to the angle and glute activation, making it a good full body press, as opposed to "isolation for the pressing muscle", however both have their uses.
I used the lift in stints when I merely had a barbell and it was an alternate to the strict floor press I also used. I see it as the push press equivalent of the floor press. For athletes, as noted in that article, creating ground force through the lower body is what makes upper body strength count in sports.
Dr Bret Contreras' wrote an article on it (listed above) on the benefit of the Bridge Bench Press.
As the picture demonstrates the bar is brought down more toward the abs.
Per Contreras the benefits are...
1) ...It stretches the pecs into their full range of motion, which means more opportunity to maximally develop them.:"
2) This exercise will help you push opponents forward in many sports, aid in strengthening the forward-arm swing portion of sprinting, and will help you climb over walls. If done explosively it'll transfer to punching power.\
Another modified method of Benching Pressing for Powerlifter is something I have gone into and Philipe does a nice job of demonstrating
A good training video that does a nice job of breaking it down is...
Head Position on The Bench Press Ft. FilipinoThunder
The head is lifted as the bar comes down. Once it touches the chest, the head is then tucked down and driven back into the bench.
As the head is driven back into the bench, the chest naturally arcs up; initiating greater momentum in driving the bar off the chest; which allow you to drive more weight off the chest.
Let look at one more interesting lost Bench Press training method that was used in the 1920's and 1930's.
I didn't know about it until 2008. Joe DeMarco (one of the founders of the Westside Training Program) demonstrated it to me.
The Belly Toss Bench Press
The Belly Bounce Bench Press in this video
This was one of the training method the Original Westside Barbell Club used in training their bench.
The bar is dropped and rebounded off the belly.
1) It was a overload method that allowed them to utilize more weight in this quazi Bench Press.
2) It was/is a method of increasing power.
The Original Westside Bell Toss Training Method attached pad to the chest to cushion some of the impact.
In my Belly Toss Bench Press Training session with DeMarco, we used...
I use the pads when performing aggressive Plyometric Bench Press Training. That means, allowing the bar to basically free fall down to my chest (obtain a bounce) and then drive the weight back up, as hard and fast as I can.
I anchor the Garden Pads around my chest an exercise band.
Using the Garden Kneeling Pads is similar performing Partial Bench Press Board Presses and getting a slight bounce off the board.
With that in mind, I have used board in performing Plyometric Bench Presses. More power is produce in bouncing the weight off the board vs the Garden Pads.
Board Plyometric Bench Pressing is like running a stable surface, like concrete; you are able to produce more force/power.
Garden Pad Plyometric Bench Pressing is somewhat like running on a slightly unstable surface, like sand; a hyperbolic example.
The softer Garden Pads end up absorbing of the force (like running in sand). Thus, less power/force is transmitted and displayed in driving the bar up in the rebound, in the concentric part of the Plyometric Bench Press.
That was my initial reaction, like most, when I was introduced to this type of aggressive Bench Press Training. It took me a while to try it and ease into it.
These aggressive type of Bench Press Training have a place in training dependent on your training objective.
Secondly, due to the aggressive nature, methods like this should be gradually eased into.